Modelling the impact of roads on regional population of Moor frogs ...

university <strong>of</strong> copenhagen
Maj-Britt Pontoppidan
Department <strong>of</strong> Biology
<strong>Modelling</strong> <strong>the</strong> <strong>impact</strong> <strong>of</strong> <strong>roads</strong> on
regional population <strong>of</strong> Moor frogs
(Rana arvalis)

FACULTY OF SCIENCE
UNIVERSITY OF COPENHAGEN
PhD <strong>the</strong>sis
Maj-Britt Pontoppidan
Section <strong>of</strong> Ecology & Evolution
Department <strong>of</strong> Biology
<strong>Modelling</strong> <strong>the</strong> <strong>impact</strong> <strong>of</strong> <strong>roads</strong> on regional
populations <strong>of</strong> Moor frogs (Rana arvalis)
A <strong>the</strong>sis submitted to <strong>the</strong> University <strong>of</strong> Copenhagen in accordance with <strong>the</strong> requirements for
<strong>the</strong> degree <strong>of</strong> <strong>the</strong> PhD at <strong>the</strong> Graduate School <strong>of</strong> Science, Faculty <strong>of</strong> Science, University <strong>of</strong>
Copenhagen, Denmark to be defended publicly before a panel <strong>of</strong> examiners
Academic advisor: Gösta Nachman
Submitted: January 2013

Preface
Preface
In this <strong>the</strong>sis I present my work carried out during a 3-year PhD fellowship funded by <strong>the</strong>
Danish Road Directorate. The objective <strong>of</strong> <strong>the</strong> project has been to develop a management tool
for assessment <strong>of</strong> <strong>the</strong> <strong>impact</strong> <strong>of</strong> <strong>roads</strong> on Moor frog populations. During my PhD-work, I have
been based at <strong>the</strong> Department <strong>of</strong> Biology, Section for Ecology and Evolution and I have been
supervised by Dr. Gösta Nachman.
The end product <strong>of</strong> <strong>the</strong> project is an individual based model called SAIA (Spatial Amphibian
Impact Assessment). The model has evolved in close and continuous dialogue with
<strong>the</strong> project group, which contains members from <strong>the</strong> Danish Nature Agency, <strong>the</strong> Road Directorate
as well as specialists on environmental <strong>impact</strong> assessments (EIA) and amphibians. Not
being a herpetologist nor road ecologist myself, <strong>the</strong>re is always <strong>the</strong> danger that <strong>the</strong> dazzling
model you have come up with is just a tiny bit far reached. During <strong>the</strong> design process, it has
been extremely important for me continuously to have <strong>the</strong> opportunity to give my model and
its components a "reality check". Hence, discussions in <strong>the</strong> project group with amphibian experts
and end users on <strong>the</strong> validity and usefulness <strong>of</strong> <strong>the</strong> model behaviour and output has been
an integrated part <strong>of</strong> <strong>the</strong> model development.
The <strong>the</strong>sis consists <strong>of</strong> a synopsis and three chapters. In <strong>the</strong> synopsis, I give an overview
<strong>of</strong> <strong>the</strong> background <strong>the</strong>ory and <strong>the</strong> model development. The chapters each contain a manuscript
submitted to a scientific journal. The manuscript in chapter one has been peer reviewed and
<strong>the</strong> enclosed version is now under revision. The two remaining manuscripts are in <strong>the</strong> process
<strong>of</strong> peer review. The appendix contains examples <strong>of</strong> SAIA’s output files.
Maj-Britt Pontoppidan
Copenhagen, January 2013
3

Index
Index
ACKNOWLEDGEMENTS ........................................................................................................................ 7
ENGLISH SUMMARY ............................................................................................................................ 9
DANSK RESUME ................................................................................................................................. 11
SYNOPSIS .............................................................................................................................. 13
BACKGROUND ................................................................................................................................... 15
Fragmentation .............................................................................................................................. 15
Connectivity .................................................................................................................................. 16
Objective ....................................................................................................................................... 18
DESIGNING SAIA .............................................................................................................................. 19
Conceptual model ......................................................................................................................... 19
The habitat patch .......................................................................................................................... 21
Dispersal behaviour ..................................................................................................................... 22
SAIA v1.0 ...................................................................................................................................... 23
CONCLUSION ..................................................................................................................................... 25
REFERENCES ...................................................................................................................................... 27
CHAPTER ONE ..................................................................................................................... 33
CHAPTER TWO .................................................................................................................... 59
CHAPTER THREE ............................................................................................................... 95
APPENDIX ........................................................................................................................... 143
5

Acknowledgements
Acknowledgements
This project would not have been possible without <strong>the</strong> goodwill and assistance <strong>of</strong> many people.
I would like to express my heartfelt thanks to all <strong>of</strong> <strong>the</strong>m:
to <strong>the</strong> Danish Road Directorate for funding <strong>the</strong> project and giving me this wonderful opportunity.
to <strong>the</strong> members <strong>of</strong> <strong>the</strong> project group: Marianne Ujvari, Martin Schneekloth, Agnete Jørgensen
and Martin Hesselsøe. It’s been a joy working with you.
to AmphiConsult for sharing your expertise with me.
to Volker Grimm and Uta Berger for introducing me to <strong>the</strong> intriguing world <strong>of</strong> NetLogo and
Individual Based <strong>Modelling</strong> as well as <strong>the</strong> beautiful region <strong>of</strong> Swiss Saxony. Special thanks to
Uta for encouraging and inspiring talks and for keeping me on <strong>the</strong> IBM-track.
to Bjørn Hermansen for patiently helping me with GIS.
to Henning Bang Madsen and Ruth Bruus Jakobsen for your readiness to help out and
your generous limousine service.
to Marianne Philipp for providing refuge in stressful times and for sharing your anemones
with me.
to all my colleagues at <strong>the</strong> section <strong>of</strong> Ecology & Evolution for good company and for so generously
letting me pick your brains and books.
And, last but not least, to my supervisor Gösta Nachman for embarking on this journey with
me and for always having an open door. I’ve enjoyed our time toge<strong>the</strong>r and I’ll miss all your
anecdotes.
7

English summary
English summary
Over <strong>the</strong> last decade a growing amount <strong>of</strong> literature has documented <strong>the</strong> severe <strong>impact</strong>s <strong>of</strong>
transport infrastructure on biodiversity, population persistence and gene flow, and <strong>the</strong>re is an
increasing awareness <strong>of</strong> <strong>the</strong> importance <strong>of</strong> finding agreement between nature conservation and
land use. To ensure ecologically sustainable road planning conservation measures must be
taken into consideration already in <strong>the</strong> earliest phases <strong>of</strong> road development. This requires adequate
tools for assessment, prevention and mitigation <strong>of</strong> <strong>the</strong> <strong>impact</strong>s <strong>of</strong> infrastructure. For this
reason <strong>the</strong> Danish Road Directorate decided to finance a PhD project with <strong>the</strong> objective <strong>of</strong>
developing a management tool that could be used to substantiate that <strong>the</strong> conservation status
<strong>of</strong> annex IV species would be unaffected by <strong>the</strong> a given road project. The purpose <strong>of</strong> <strong>the</strong> project
was to provide a standardized and scientifically well founded basis for decisions concerning
road lay-out and mitigation measures. As model species was chosen <strong>the</strong> Moor frog (Rana
arvalis). Populations <strong>of</strong> Moor frogs are assumed to follow a pattern <strong>of</strong> metapopulation dynamics,
with colonisation, extinction and recolonisation <strong>of</strong> suitable habitat patches. Thus,
road constructions must be expected to have implication on both local and regional persistence;
<strong>the</strong> former due to habitat destruction, <strong>the</strong> latter because <strong>of</strong> disrupted dispersal between
subpopulations due to barrier effects.
The result <strong>of</strong> <strong>the</strong> project was <strong>the</strong> development <strong>of</strong> <strong>the</strong> model presented in this <strong>the</strong>sis. The
model, called SAIA (Spatial Amphibian Impact Assessment), considers a landscape mosaic <strong>of</strong>
breeding habitat, summer habitat and uninhabitable land. As input I use a GIS-map <strong>of</strong> <strong>the</strong>
landscape with information on land cover. In addition, data on observed frog populations in
<strong>the</strong> survey area are needed. The dispersal <strong>of</strong> juvenile frogs is simulated by means <strong>of</strong> individual-based
modelling, while a population-based model is used for simulating long-term population
dynamics. In combination, <strong>the</strong> two types <strong>of</strong> models generate output on landscape connectivity
and population viability. To assess road <strong>impact</strong>s two scenarios have to be constructed
and analysed. The first scenario should be a map <strong>of</strong> <strong>the</strong> area as it is before <strong>the</strong>
planned road construction (scenario 0). This analysis measures <strong>the</strong> ecological performance <strong>of</strong>
<strong>the</strong> original landscape and is a reference against which o<strong>the</strong>r scenarios are to be compared.
The second map (scenario 1) should show <strong>the</strong> landscape as it is expected to be after <strong>the</strong> road
constructions. In combination, <strong>the</strong> analyses <strong>of</strong> scenario 0 and scenario 1 make it possible to
assess <strong>the</strong> effect <strong>of</strong> road construction on connectivity and population persistence. The analyses
9

English summary
also constitute <strong>the</strong> basis for planning <strong>of</strong> mitigation measures. Analyses and comparisons <strong>of</strong>
several alternative road projects can identify <strong>the</strong> least harmful solution. The effect <strong>of</strong> mitigation
measures, such as new breeding ponds and tunnels, can be evaluated by incorporating
<strong>the</strong>m in <strong>the</strong> maps, <strong>the</strong>reby enhancing <strong>the</strong> utility <strong>of</strong> <strong>the</strong> model as a management tool in Environmental
Impact Assessments.
The <strong>the</strong>sis consists <strong>of</strong> a synopsis and three manuscripts for scientific journals. An appendix
contains examples <strong>of</strong> <strong>the</strong> result files SAIA produces. In <strong>the</strong> synopsis, I give an overview
<strong>of</strong> <strong>the</strong> background <strong>the</strong>ory and <strong>the</strong> conceptual model development.
In <strong>the</strong> first manuscript I introduce an alternative patch concept, <strong>the</strong> complementary
habitat patch, and use a simple model to explore how intra-patch heterogeneity affects immigration
and emigration probabilities. I find that <strong>the</strong> realised connectivity depends on internal
structure <strong>of</strong> both <strong>the</strong> target and <strong>the</strong> source patch as well as on how habitat quality is affected
by patch structure. Although fragmentation is generally thought to have negative effects on
connectivity, <strong>the</strong> results suggest that, depending on patch structure and habitat quality, positive
effects on connectivity may occur.
The second manuscript uses a light-version <strong>of</strong> SAIA and explores how changes in road
mortality and road avoidance behaviour affect local and regional connectivity in a population
<strong>of</strong> Moor frogs. The results indicate that road mortality has a strong negative effect on regional
connectivity, but only a small effect on local connectivity. Regional connectivity is positively
affected by road avoidance and <strong>the</strong> effect becomes more pronounced as road mortality decreases.
Road avoidance also has a positive effect on local connectivity. When road avoidance
is total and <strong>the</strong> road functions as a 100% barrier regional connectivity is close to zero, while
local connectivity exhibit very elevated values. The results suggest that <strong>roads</strong> may affect not
only regional or metapopulation dynamics but also have a direct effect on local population
dynamics.
The third manuscript describes <strong>the</strong> full SAIA model. By means <strong>of</strong> a case study I demonstrate
how SAIA can be used for assessment <strong>of</strong> road <strong>impact</strong> and evaluation <strong>of</strong> which management
measures would be best to mitigate <strong>the</strong> effect <strong>of</strong> landscape fragmentation caused by
road constructions.
10

Dansk resumé
Dansk resume
En stadigt tættere infrastruktur præger vores landskaber og er blevet en kraftig trussel mod
biodiversiteten. Der er en stigende bevids<strong>the</strong>d om nødvendigheden af at anlæggelse af veje
må være bæredygtig. For at opnå dette er det nødvendigt allerede i de tidligste faser af vejprojekter
at inddrage overvejelser omkring bevarelsesforanstaltninger. Dette kræver, at der er
passende værktøjer til rådighed, hvormed det er muligt at vurderer effekten på naturen af såvel
den kommende vej som mulige afværgeforanstaltninger. På denne baggrund besluttede
Vejdirektoratet at finansierer et PhD projekt, hvis formål var at udvikle et modelværktøj, der
kunne underbygge et ensartet og fagligt baseret beslutningsgrundlag ved valg af linjeføring.
Endvidere skulle værkstøjet kunne understøtte beslutninger vedrørende afværgeforanstaltninger,
deres antal og placering. Spidssnudet frø (Rana arvalis) blev valgt som model-art. En
population af Spidssnudet frø antages at bestå af et netværk af delpopulationer, samt at følge
en metapopulationsdynamik med kontinuert kolonisering, udryddelse og rekolonisering af
egnede habitatområder. Nye vejanlæg kan forventes at påvirke en populations levedygtighed,
både lokalt ved at ødelægge habitatområder og regionalt ved at virke som en barriere for
spredning af individer mellem delpopulationerne.
Resultatet af projektet blev modellen som præsenteres i denne afhandling. Modellen,
kaldet SAIA (Spatial Amphibian Impact Assessment), tager udgangspunkt i et landskab bestående
af en mosaik af ynglehabitat, sommer habitat og ubeboeligt habitat. Som input til modellen
bruger jeg GIS-kort, der indeholder informationer om arealanvendelse. Derudover skal
der bruges data på populationen af Spidssnudet frø i undersøgelsesområdet. Jeg bruger individ-baseret
modellering til at simulerer spredningen af nyforvandlede frøer samt en populationsbaseret
model til at simulerer populationsdynamikken i de enkelte populationer. Tilsammen
genererer de to modeller output om landskabets konnektivitet og om populationens levedygtighed.
For at kunne evaluerer konsekvenserne af et kommende vejanlæg kræves to scenarier.
Det første scenarie fungerer som reference og skal være et kort over landskabet, som det ser
ud før det planlagte vejanlæg. Det andet scenarie er et kort over landskabet, som det forventes
at se ud, når vejprojektet er udført. Ved at sammenligne resultaterne fra de to analyser er det
muligt at vurdere, hvordan vejanlægget vil påvirker landskabets konnektivitet og frø-
11

Dansk resumé
populationens levedygtighed. Analyserne kan samtidigt danne basis for planlægning af afværgeforanstaltninger.
Analyser og evaluering af scenarie med alternative lineføringer eller
forskellige afværgeforanstaltninger giver mulighed for identificerer de bedste løsninger og
resultaterne kan indgå i f.eks. VVM-undersøgelser.
Afhandling består af en synopsis, tre videnskabelige artikler samt et appendiks det indeholder
eksempler på de resultat-filer SAIA genererer. I synopsen giver jeg et overblik over
den konceptuelle udvikling af SAIA-modellen samt den bagvedliggende teori.
I den første artikel beskriver jeg, hvordan et habitatområde kan betragtes som sammensat
af forskellige habitat typer og introducerer et alternativt habitat begreb, det komplementære
habitatområde. Jeg bruger en simpel model til at udforske, hvordan sammensætningen af et
komplementært habitat påvirker sandsynligheden for immigration til og emigration fra habitatet.
Resultaterne viser, at strukturen såvel som kvaliteten i et habitatområde har stor betydning
for landskabets konnektivitet. Desuden finder jeg, at fragmentering under visse forhold kan
have en positiv effekt på konnektiviteten.
I den anden artikel bruger jeg en forenklet version af SAIA til at afsøge, hvordan ændringer
i vejdødelighed og dyrs evne til at undvige veje påvirke konnektiviteten mellem bestande,
både lokalt og regional. Resultaterne viser, at vejdødeligheden har en kraftig negativ
effekt på regional konnektivitet, men kun lille effekt lokalt. Afværgeadfærd har en positiv
effekt på både regional og lokal konnektivitet - effekten er dog mest udtalt, når vejdødeligheden
er lav. Hvis afværgeadfærden er så kraftig, at vejen reelt fungerer som en 100 % barrierer,
er den regional konnektivitet dog tæt på nul, mens det lokale konnektivitet opnår meget høje
værdier. Resultaterne peger på, at veje kan påvirke populationsdynamikken både lokalt og
regionalt.
Den tredje artikel beskriver den fulde SAIA model. Ved hjælp af et case-studie demonstrerer
jeg ,hvordan modellen kan anvendes til vurdere effekten af et planlagt vejanlæg på en
bestand af spidssnudet frø, samt hvilke afværgeforanstaltninger der kan modvirke effekten
12

SYNOPSIS

Synopsis
Background
Roads are everywhere. An extensive and expanding infrastructural network connects human
activities; it enables us to reach <strong>the</strong> fur<strong>the</strong>st parts <strong>of</strong> <strong>the</strong> world and gives us access to <strong>the</strong> resources
we need. They bring us to our friends and family, our working places and recreational
activities. We use <strong>the</strong>m to go shopping and to enjoy a walk in <strong>the</strong> forest. But while infrastructure
binds <strong>the</strong> human society toge<strong>the</strong>r, <strong>roads</strong> also act as barriers – cutting through home
ranges <strong>of</strong> animals and crossing <strong>the</strong>ir migration or dispersal routes. Roads restrict animals’
access to resources and affect <strong>the</strong>ir behaviour and movement patterns [1, 2].
Today’s huge network <strong>of</strong> <strong>roads</strong> is a major threat to many species. Animals trying to
cross a road experience a very high mortality risk, and many populations <strong>of</strong> (mostly large)
mammals, birds and amphibians are negatively affected by road killings [3-7]. Especially species
with large ranges or with high mobility seem to be most vulnerable to road mortality [8,
9]. Increased mortality caused by <strong>roads</strong> may not only reduce population sizes, but – at least in
amphibians – also shift age distributions toward younger age classes resulting in reduced reproduction
[10]. Even though road killings reduce road crossing some movement across <strong>the</strong>
road may occur; <strong>the</strong> barrier effect will not be total unless road mortality is 100%.
Many species are able to detect <strong>roads</strong> and <strong>the</strong>reby actively avoid <strong>the</strong>m [11]. While this
behaviour reduces <strong>the</strong> risk <strong>of</strong> road-killing, it also limits access to resources and fur<strong>the</strong>r isolates
populations on one side <strong>of</strong> <strong>the</strong> road [12]. Thus, animals’ behavioural responses to <strong>roads</strong> may
enhance <strong>the</strong> barrier effect <strong>of</strong> <strong>the</strong> road. Consequently, road effects on population persistence
may depend on <strong>the</strong> interaction between road mortality and road avoidance [13, 14].
Fragmentation
The barrier effect <strong>of</strong> <strong>roads</strong> fragments <strong>the</strong> natural habitat <strong>of</strong> species; consistently dividing continuous
areas <strong>of</strong> habitat into smaller and more isolated fragments. Today, fragmentation and
habitat loss are considered <strong>the</strong> greatest threat to biodiversity and population persistence [15].
All else being equal, habitat loss will reduce <strong>the</strong> amount <strong>of</strong> resources and consequently also
population sizes [16]. Fur<strong>the</strong>rmore, fragmentation divides a population into several smaller
subpopulations. Small populations are more vulnerable to environmental and demographic
stochasticity and thus have a higher risk <strong>of</strong> extinction. [17-20] Conversion <strong>of</strong> a continuous
habitat area into several smaller also results in more edge area and a higher perimeter:area
15

Synopsis
ratio. This affects <strong>the</strong> quality <strong>of</strong> a habitat patch and <strong>the</strong> area effectively available to a population
may be reduced [21]. The fragmentation process changes <strong>the</strong> landscape composition by
substituting habitat with non-habitat, and this may affect <strong>the</strong> movements <strong>of</strong> animals. Individuals
may not move into non-habitat at all, or if <strong>the</strong>y do <strong>the</strong> changes in <strong>the</strong> spatial arrangement
<strong>of</strong> habitat fragments may increase <strong>the</strong> time it takes to find resources, sometimes causing significantly
higher transit mortalities [22-26]. Hence, fragmentation impedes movement and
isolates habitat fragments from each o<strong>the</strong>r. However, movement is an important part <strong>of</strong> many
organisms’ ecology. Individuals need to move to find necessary resources such as food, protection,
mates, breeding sites or space, and <strong>the</strong> success in finding <strong>the</strong>se resources will determine
<strong>the</strong> density and distribution <strong>of</strong> a population [27, 28]. Thus, <strong>the</strong> viability <strong>of</strong> a population
will depend on how well resource patches are linked toge<strong>the</strong>r, and <strong>the</strong> term “connectivity” is
frequently used to describe <strong>the</strong> strength <strong>of</strong> those linkages.
Connectivity
Connectivity depends on <strong>the</strong> patchiness and <strong>the</strong> spatial structure <strong>of</strong> <strong>the</strong> landscape and it is
<strong>the</strong>refore a central concept in “spatial” disciplines like Metapopulation ecology and Landscape
ecology [29, 30]. Even though both disciplines are concerned with <strong>the</strong> effect <strong>of</strong> connectivity
on population persistence, <strong>the</strong>ir focus is not quite <strong>the</strong> same [31].
Metapopulation ecology considers populations consisting <strong>of</strong> a network <strong>of</strong> subpopulations.
Some or all <strong>of</strong> <strong>the</strong> subpopulations repeatedly experience decreasing population sizes or
even extinction and may be rescued or recolonized by immigrants from neighbouring subpopulations.
The persistence <strong>of</strong> <strong>the</strong> whole population relies on <strong>the</strong> dispersal <strong>of</strong> individuals
among subpopulations. Within <strong>the</strong> metapopulation framework subpopulations are considered
to inhabit patches <strong>of</strong> homogenous habitat embedded in a homogenous matrix <strong>of</strong> non-habitat.
Connectivity is regarded as <strong>the</strong> probability <strong>of</strong> a local population receiving an immigrant from
ano<strong>the</strong>r population. In its basic form connectivity depends on <strong>the</strong> distance to and <strong>the</strong> size <strong>of</strong>
<strong>the</strong> donor population (<strong>of</strong>ten measured as <strong>the</strong> area <strong>of</strong> <strong>the</strong> habitat patch) [29, 32-35], and thus
connectivity is defined as a property <strong>of</strong> <strong>the</strong> subpopulation (or habitat patch).
In Landscape ecology <strong>the</strong> focus is on <strong>the</strong> composition <strong>of</strong> <strong>the</strong> landscape. Habitat patches
do not exist in a homogenous background matrix but is part <strong>of</strong> a landscape mosaic <strong>of</strong> different
habitats and structures [27]. The movement paths <strong>of</strong> individuals depend on <strong>the</strong> spatial arrangement
<strong>of</strong> habitats. Some habitat types are avoided, o<strong>the</strong>rs are preferred; structures may
16

Synopsis
obstruct accessibility or incur high mortality. Thus, accessibility <strong>of</strong> resource patches does not
only depend on distance but also on <strong>the</strong> properties and configuration <strong>of</strong> <strong>the</strong> matrix in between
patches [22, 36]. Landscape ecology defines connectivity as <strong>the</strong> degree to which <strong>the</strong> landscape
facilitates or impedes movement among resource patches [30]. Connectivity is regarded as a
landscape property describing <strong>the</strong> permeability <strong>of</strong> <strong>the</strong> mosaic, and opposite to metapopulation
ecology does not contain any demographic indicators [37].
Maintaining connectivity is generally regarded as an essential goal <strong>of</strong> environmental
conservation [38], and methods for quantifying connectivity are, thus, important. Improved
computer power, advancing use <strong>of</strong> remote sensing and GIS have allowed for increasing use <strong>of</strong>
spatially explicit methods, and <strong>the</strong>re is now a range <strong>of</strong> tools available for assessing fragmentation
or connectivity [39-41]. Graph and circuit <strong>the</strong>oretical approaches have been used to construct
networks with habitat patches represented as nodes and links between nodes (edges)
representing inter-node connectivity [42-44]. Network characteristics can <strong>the</strong>n be used as metrics
<strong>of</strong> landscape connectivity. O<strong>the</strong>r methods are based on metapopulation <strong>the</strong>ory and use
incidence functions to model connectivity [45, 46]. In all <strong>of</strong> <strong>the</strong> above mentioned approaches
connectivity between habitat patches can be based on dispersal distance alone [47], but o<strong>the</strong>r
species specific parameters can be included. This can be indices on population size or habitat
resistance to movement [48]. Fur<strong>the</strong>rmore, least cost analysis can be used to substitute
Euclidean distances with optimal movement paths between patches [49-51].
Recently <strong>the</strong>re has been a growing interest in individual (or agent) based methods
(IBM) in ecological modelling [52-55]. Recognising that movement patterns and, thus, also
connectivity depend on individual behaviour, landscape configuration and <strong>the</strong>ir interaction
[22, 40] individual based modelling seems a promising method for assessment <strong>of</strong> connectivity.
IBM has been used to assess <strong>the</strong> effect <strong>of</strong> <strong>roads</strong> on dispersal success <strong>of</strong> for example
Eurasian lynx [56] and Elk [57]. Graf, et al. [58] assessed <strong>the</strong> connectivity between patchy
populations <strong>of</strong> Capercaillie embedded in a mountainous landscape. A generic individual based
model to simulate dispersal (J-Walk) has been developed by Gardner and Gustafson [59] and
used to estimate connectivity <strong>of</strong> a wide range <strong>of</strong> species, e.g. Delmarva fox squirrel [60],
Black bears [61] and American marten [62]. FunCon [63] is ano<strong>the</strong>r individual based connectivity
tool which can be applied on bird species.
17

Synopsis
Objective
Over <strong>the</strong> last decade a growing amount <strong>of</strong> literature has documented <strong>the</strong> severe <strong>impact</strong>s <strong>of</strong>
transport infrastructure on biodiversity, population persistence and gene flow [1, 2, 12, 64-
66], and <strong>the</strong>re is an increasing awareness <strong>of</strong> <strong>the</strong> importance <strong>of</strong> finding agreement between
nature conservation and land use. In Europe, <strong>the</strong> EU Habitats directive enjoins member states
to safeguard <strong>the</strong> ecological performance <strong>of</strong> breeding sites and resting places <strong>of</strong> species protected
by <strong>the</strong> Habitat directive annex IV [67]. Fur<strong>the</strong>rmore, according to EU legislation, all
major projects, including infrastructure projects, are subject to Environmental Impact Assessment
(EIA) [68]. Infra Eco Network Europe (IENE), a network <strong>of</strong> specialists, governmental
agencies, scientists and NGOs, enables cross-boundary and interdisciplinary cooperation
on issues regarding ecologically sustainable transportation systems. A prominent result from
IENE has been <strong>the</strong> European review <strong>of</strong> Habitat Fragmentation due to Linear Transportation
Infrastructure [69] as well as <strong>the</strong> European handbook on sustainable road planning [70]; both
published by <strong>the</strong> European Communities.
To ensure ecologically sustainable road planning, conservation measures must be taken
into consideration already in <strong>the</strong> earliest phases <strong>of</strong> road development. This requires adequate
tools for assessment <strong>of</strong> both <strong>the</strong> <strong>impact</strong>s <strong>of</strong> infrastructure and <strong>the</strong> effect <strong>of</strong> mitigation measures
[71-73]. For this reason <strong>the</strong> Danish Road Directorate decided to finance a PhD project
with <strong>the</strong> objective <strong>of</strong> developing a management tool which could be used to substantiate that
<strong>the</strong> conservation status <strong>of</strong> annex IV species would remain unaffected by a given road project
[67]. The Moor frog (Rana arvalis) was chosen as <strong>the</strong> model species. This pond breeding amphibian
is listed in annex IV <strong>of</strong> <strong>the</strong> Habitats directive, but is relatively common, at least in <strong>the</strong>
eastern part <strong>of</strong> Denmark. Therefore, <strong>the</strong>re will <strong>of</strong>ten be a need to assess <strong>the</strong> <strong>impact</strong> <strong>of</strong> new
road constructions on local populations <strong>of</strong> Moor frogs.
The purpose <strong>of</strong> <strong>the</strong> project was to provide a standardized and scientifically well founded
basis for decisions concerning road lay-out and mitigation measures. The management tool
should support decision making by enabling caseworkers
to find <strong>the</strong> optimal location and road lay-out for a specific species
to assess <strong>the</strong> need for mitigation measures, such as tunnels, fences and compensation habitat
for a specific species
to identity <strong>the</strong> best location for tunnels, fences and compensation habitat
18

Synopsis
to evaluate <strong>the</strong> effect <strong>of</strong> mitigation measure on ecological performance
The project resulted in <strong>the</strong> development <strong>of</strong> a spatially explicit and individual based model
called SAIA (Spatial Amphibian Impact Assessment).
Designing SAIA
When assessing ecological performance <strong>the</strong> most obvious metrics are population size and
persistence [74]. In general, <strong>roads</strong> can affect amphibian populations in three ways – by destruction
and fragmentation <strong>of</strong> habitat, by road kills, or by disruption <strong>of</strong> movement patterns
[5, 7, 75]. Thus, <strong>the</strong> first step in <strong>the</strong> model development has been to construct a conceptual
model <strong>of</strong> <strong>the</strong> possible effects <strong>of</strong> road construction on a population <strong>of</strong> Moor frogs.
Conceptual model
The Moor frog is a pond breeding amphibian that needs aquatic as well as terrestrial habitat to
complete its life cycle. The first phase <strong>of</strong> <strong>the</strong> life cycle, as egg and larva, takes place in shallow
<strong>of</strong>ten ephemeral ponds. The remaining part takes place in terrestrial habitat while ponds
are only visited during breeding [76, 77]. The life cycle <strong>of</strong> <strong>the</strong> Moor frog is characterized by
two types <strong>of</strong> movement: migration, <strong>the</strong> seasonal intrapopulational movement <strong>of</strong> adult individuals
between summer habitat and breeding ponds and dispersal, <strong>the</strong> interpopulational
movement <strong>of</strong> <strong>the</strong> newly metamorphosed frogs away from <strong>the</strong>ir natal pond [77-81]. Many amphibian
populations are considered to be organised as a metapopulation [82-85]. This has not
been studied explicitly for Moor frogs, but it is generally assumed by experts (pers. comm.)
that Moor frogs form regional networks <strong>of</strong> subpopulations. Thus, regional population persistence
depends on successful dispersal between subpopulations.
Given this background, it seems reasonable to assume that <strong>roads</strong> can affect <strong>the</strong> persistence
<strong>of</strong> Moor frog populations in several ways (Fig 1):
destruction <strong>of</strong> aquatic habitat
destruction <strong>of</strong> terrestrial habitat
fragmentation <strong>of</strong> terrestrial habitat
impaired migration between aquatic and terrestrial habitat
impaired dispersal between subpopulations
19

Synopsis
The first effect prevents <strong>the</strong> subpopulation from reproducing and is considered equal to destruction
<strong>of</strong> <strong>the</strong> subpopulation. The next three effects reduce <strong>the</strong> amount and quality <strong>of</strong> accessible
terrestrial habitat, and hence, <strong>the</strong> size <strong>of</strong> <strong>the</strong> population that can be sustained by <strong>the</strong> habitat.
The last effect reduces <strong>the</strong> probability <strong>of</strong> (re)colonization <strong>of</strong> habitat patches, resulting in
isolation <strong>of</strong> subpopulations.
Figure 1
Conceptual model <strong>of</strong> road effects on a regional
Moor frog population. Dotted lines
delimit subpopulations, blue dots represent
breeding ponds and green areas are summer
habitat fragments.
Processes affected by <strong>roads</strong> are outlined in
red
To incorporate local as well regional population dynamics into <strong>the</strong> model, I combine individual
based modelling with a population dynamics model. The local population dynamics
in each pond are simulated by use <strong>of</strong> an age-based Leslie matrix and are affected by <strong>the</strong> size
and quality <strong>of</strong> <strong>the</strong> breeding pond and summer habitat. Regional effects are assessed by simulating
dispersing frogs’ behavioural responses to land cover and structure while moving
through <strong>the</strong> landscape. This provides estimates <strong>of</strong> immigration probabilities between subpopulations.
These estimates reflect <strong>the</strong> connectivity <strong>of</strong> <strong>the</strong> landscape to be entered into <strong>the</strong>
local dynamics <strong>of</strong> each pond as immigration rates (Fig. 2).
Figure 2
Elements <strong>of</strong> SAIA
20

Synopsis
The connectivity measure <strong>of</strong> SAIA does not adhere strictly to ei<strong>the</strong>r <strong>of</strong> <strong>the</strong> definitions
used in metapopulation or landscape ecology. Ra<strong>the</strong>r it is an attempt to find a “third” way
[31]. SAIA’s connectivity measure considers dispersal between subpopulations and, thus,
adopts metapopulation ecology’s patch based focus. However, as in landscape ecology, population
size (or any o<strong>the</strong>r demographic indicator) does not enter into <strong>the</strong> connectivity measure.
In SAIA, connectivity is solely a function <strong>of</strong> landscape configuration and animal behaviour
and is measured as <strong>the</strong> probability <strong>of</strong> an individual finding its way from habitat patch A to
habitat patch B. Moreover, SAIA’s connectivity measure is an index <strong>of</strong> <strong>the</strong> potential connectivity
between all habitat patches, whe<strong>the</strong>r <strong>the</strong>y are populated or not. The population based
model links <strong>the</strong> potential connectivity with local population dynamics, and estimated abundances
and persistence probabilities can be regarded as a result <strong>of</strong> <strong>the</strong> realised connectivity.
The habitat patch
An important characteristic <strong>of</strong> SAIA is how <strong>the</strong> habitat patch <strong>of</strong> a subpopulation <strong>of</strong> Moor
frogs is represented. In most studies measuring or modelling connectivity in regional populations
<strong>of</strong> amphibians, <strong>the</strong> breeding pond is used as <strong>the</strong> spatial unit <strong>of</strong> a subpopulation [85]. As
Moor frogs mostly breed in <strong>the</strong> same pond every year, SAIA also considers <strong>the</strong> pond as <strong>the</strong>
potential site <strong>of</strong> a subpopulation [86]. However, <strong>the</strong> attributes <strong>of</strong> <strong>the</strong> breeding pond alone will
not be an adequate descriptor <strong>of</strong> a subpopulation’s habitat patch. Outside <strong>the</strong> breeding season,
<strong>the</strong> frogs reside in adequate terrestrial habitat (summer habitat) usually within a distance <strong>of</strong>
400 m from <strong>the</strong> pond (defined as migration distance) [77, 78]. Whereas <strong>the</strong> size and quality <strong>of</strong>
<strong>the</strong> breeding pond may affect <strong>the</strong> reproductive output [87], it is reasonable to assume that
adult abundance will depend on <strong>the</strong> amount and quality <strong>of</strong> <strong>the</strong> terrestrial habitat in which <strong>the</strong>
frogs live during summer. Consequently, in SAIA <strong>the</strong> habitat patch <strong>of</strong> a subpopulation <strong>of</strong>
Moor frogs is defined as complementary habitat patch consisting <strong>of</strong> a breeding pond and all
accessible summer habitat fragments within migration distance. Accessibility is important in
this context. Roads (or o<strong>the</strong>r impregnable structures) can function as barriers preventing access
to resources on <strong>the</strong> opposite side [88]. Thus, <strong>the</strong> summer habitat available for <strong>the</strong> frogs is
restricted by linear infrastructure. Conversely, construction <strong>of</strong> underpasses can re-establish <strong>the</strong>
connection with isolated habitat fragments (Fig. 3).
21

Synopsis
A Figure 3
Illustration <strong>of</strong> how accessible summer habitat is identified.
Blue circle is a pond; dotted circle represents maximum migration
distance. Green areas are accessible summer habitat
while shaded areas are inaccessible summer habitat.
B
A) All summer habitat within migration distance is regarded
as accessible
B) Road traversing <strong>the</strong> habitat prevents access to summer
habitat on <strong>the</strong> opposite side <strong>of</strong> <strong>the</strong> road
C) Structures breaking <strong>the</strong> road such as underpasses again
C
permits access to summer habitat on <strong>the</strong> opposite side <strong>of</strong> <strong>the</strong>
road.
In <strong>the</strong> model, <strong>the</strong> carrying capacity <strong>of</strong> a habitat patch is determined by <strong>the</strong> area <strong>of</strong> accessible
summer habitat, and adult survival is modelled as depending on <strong>the</strong> frog density <strong>of</strong> <strong>the</strong>
summer habitat. The effective area <strong>of</strong> <strong>the</strong> summer habitat depends on <strong>the</strong> degree <strong>of</strong> fragmentation
and, thus, <strong>the</strong> area <strong>of</strong> summer habitat is weighted by <strong>the</strong> amount <strong>of</strong> edges [89]. In real
landscapes summer habitat is <strong>of</strong>ten shared by several breeding ponds, and in <strong>the</strong> model <strong>the</strong>
frog density <strong>of</strong> a single summer habitat cell, <strong>the</strong>refore, depends on <strong>the</strong> population sizes <strong>of</strong> all
<strong>the</strong> breeding ponds sharing <strong>the</strong> summer habitat.
Dispersal behaviour
Individual based modelling is a little like story telling. Based on <strong>the</strong> available research on
behaviour, patterns <strong>of</strong> abundance, distribution etc, you try to think like your species. And <strong>the</strong>
model becomes your story <strong>of</strong> how you believe individuals <strong>of</strong> <strong>the</strong> modelled species experience
and react to <strong>the</strong> set <strong>of</strong> conditions and circumstances constituting <strong>the</strong>ir environment. In more
scientific terms, models can be regarded as hypo<strong>the</strong>ses [55] and, thus, SAIA is my hypo<strong>the</strong>sis
on how newly metamorphosed frogs leave <strong>the</strong>ir natal pond and move through <strong>the</strong> landscape
until <strong>the</strong>y settle in a new habitat patch.
Young frogs have no prior knowledge <strong>of</strong> <strong>the</strong> landscape <strong>the</strong>y disperse into. While dispersing
frogs may have an innate urge to move away from <strong>the</strong>ir natal pond, <strong>the</strong>ir movements
22

Synopsis
are also assumed to be affected by <strong>the</strong>ir immediate concern <strong>of</strong> staying alive [77, 80, 90]. Thus,
movement decisions are usually centred on <strong>the</strong> environmental cues, which guide <strong>the</strong> animals
into habitat where survival probabilities are high. Very little is known about <strong>the</strong> dispersal <strong>of</strong>
juveniles. Dispersal distances are recorded to be between a few hundred meters up to 1-2
kilometres [77, 91, 92], but what triggers <strong>the</strong> decision to stop and settle down
Adult frogs show a high degree <strong>of</strong> site fidelity in regard to breeding pond and summer
habitat, and juvenile frogs appear to inhabit <strong>the</strong> same summer habitat as <strong>the</strong> adults [77, 86, 93,
94]. During breeding migrations adults <strong>of</strong>ten exhibit quite goal-oriented movements, and
some juveniles seem to follow adult frogs towards <strong>the</strong> breeding ponds although <strong>the</strong>y do not
enter <strong>the</strong> ponds <strong>the</strong>mselves [77, 90]. Juvenile frogs have to stay alive for at least two years
before <strong>the</strong>y start breeding. The above observations suggest that juvenile frogs spend <strong>the</strong> first
couple <strong>of</strong> years in <strong>the</strong> summer habitat learning to know and navigate in <strong>the</strong> habitat patch. Thus
<strong>the</strong> primary goal <strong>of</strong> dispersing juveniles must be to find summer habitat where <strong>the</strong>y can survive
until maturity. The next step will <strong>the</strong>n be to find a suitable breeding pond. <strong>Modelling</strong> <strong>the</strong>
dispersal behaviour, I <strong>the</strong>refore assume that it is <strong>the</strong> presence <strong>of</strong> summer habitat ra<strong>the</strong>r than
breeding ponds that triggers <strong>the</strong> settling behaviour. When a dispersing frog encounters summer
habitat it may decide to stop moving and settle in <strong>the</strong> new habitat, without knowing
whe<strong>the</strong>r <strong>the</strong>re is a breeding pond nearby or not.
SAIA v1.0
The resulting model, SAIA v1.0, is meant to be a strategic management tool supporting decision-making.
Fur<strong>the</strong>rmore, it is meant to be used by non-specialists. Therefore, it should be
intuitively understandable, flexible, easy to use and with an output that can be interpreted
without much effort.
The workflow is simple: a GIS map <strong>of</strong> <strong>the</strong> relevant area must be constructed and converted
into a text file; <strong>the</strong>n imported into SAIA and <strong>the</strong> analysis can be started. After <strong>the</strong>
simulations, SAIA generates several types <strong>of</strong> output in <strong>the</strong> form <strong>of</strong> text files and shape files to
be used in GIS (Fig. 4).
23

Synopsis
Figure 4
SAIA’s workflow
At least two scenarios have to be constructed to carry out a meaningful analysis. The
first scenario should be a map <strong>of</strong> <strong>the</strong> area as it is before <strong>the</strong> planned road construction (scenario
0). This analysis measures <strong>the</strong> ecological performance <strong>of</strong> <strong>the</strong> original landscape and is a
reference against which o<strong>the</strong>r scenarios are to be compared. The second map (scenario 1)
should show <strong>the</strong> landscape as it is expected to be after <strong>the</strong> road constructions. This will typically
involve drawing <strong>the</strong> new road or, in case <strong>of</strong> a road expansion, changing <strong>the</strong> properties <strong>of</strong>
<strong>the</strong> original road. Breeding ponds destroyed by <strong>the</strong> construction work are removed from <strong>the</strong>
map. More indirect effects such as reduced habitat quality close to <strong>the</strong> road or expected
changes in traffic intensity (and thus road mortality) <strong>of</strong> adjacent <strong>roads</strong> can also be incorporated
in <strong>the</strong> map. In combination, <strong>the</strong> analyses <strong>of</strong> scenario 0 and scenario 1 make it possible to
assess <strong>the</strong> effect <strong>of</strong> road construction on connectivity and population persistence which constitute
<strong>the</strong> basis for planning <strong>of</strong> mitigation measures. Hereafter, additional scenarios with alternative
suggestions for mitigation measures can be constructed, analysed and compared.
As input data SAIA needs two text file; one file to construct <strong>the</strong> land cover map and a
one file containing data about <strong>the</strong> potential breeding ponds in <strong>the</strong> area. The data in <strong>the</strong> input
files have to be structured in a specific way, but <strong>the</strong>re are no special requirements on which
s<strong>of</strong>tware to be used when constructing <strong>the</strong> files. In this project, <strong>the</strong> land cover maps are based
on several GIS layers describing <strong>roads</strong>, buildings, nature reserves, fallows, fields and so on,
while data on breeding ponds originate from field surveys. The construction <strong>of</strong> land cover
maps has not been entirely trivial as data had to be obtained from many different digital
24

Synopsis
sources. The consultancy firm AmphiConsult has been responsible for <strong>the</strong> job and has developed
a standard protocol for construction <strong>of</strong> land cover maps to be used with SAIA [95]. Even
though, map construction has not been part <strong>of</strong> my PhD project I have been involved to ensure
<strong>the</strong> compatibility with SAIA.
SAIA produces output regarding connectivity, population dynamics as well as <strong>the</strong> results
<strong>of</strong> a cluster analysis based on <strong>the</strong> connectivity matrix (examples <strong>of</strong> <strong>the</strong> output files can
be found in <strong>the</strong> appendix):
A text file with descriptive statistics on regional connectivity, abundance and population
persistence probability as well as descriptive statistics on abundance and persistence probability
<strong>of</strong> individual pond populations.
A text file containing information on clusters and <strong>the</strong>ir pond members as well as connectivity
within and between clusters
In addition, SAIA produces several GIS data files for graphic display and fur<strong>the</strong>r analysis in
GIS s<strong>of</strong>tware:
A point-data set with information on mean estimated abundance and population persistence
probability <strong>of</strong> <strong>the</strong> ponds.
Vector-data set with information about immigration probability between ponds (connectivity
network)
Vector-data set with information about cluster configuration
Conclusion
The following three chapters contain manuscripts representing different stages <strong>of</strong> <strong>the</strong> modelling
process. In <strong>the</strong> first manuscript, I use a simple model to explore <strong>the</strong> concept <strong>of</strong> <strong>the</strong> complementary
habitat patch and how intra-patch heterogeneity affects immigration and emigration
probabilities. This manuscript has been submitted to <strong>the</strong> Open Access journal “Web
Ecology” and been peer-reviewed. It is now under revision to be resubmitted soon. The second
manuscript uses a light-version <strong>of</strong> SAIA and explores how changes in levels <strong>of</strong> road
avoidance and road mortality affect connectivity locally as well as regionally. The third
manuscript describes <strong>the</strong> full SAIA model. By means <strong>of</strong> a case study, I demonstrate how
SAIA can be used for assessing which management measures would be best to mitigate <strong>the</strong>
25

Synopsis
effect <strong>of</strong> landscape fragmentation caused by road constructions. These last two manuscripts
are submitted to <strong>the</strong> Open Access journal “Nature Conservation”.
<strong>Modelling</strong> is a never-ending story and <strong>the</strong> name “SAIA v1.0” implies <strong>the</strong> possibility <strong>of</strong>
a version 2.0. In <strong>the</strong> coming months, SAIA will be implemented as a planning tool in <strong>the</strong> Danish
Road Directorate and this will be <strong>the</strong> real test <strong>of</strong> SAIA. As a variety <strong>of</strong> landscapes are being
analysed, <strong>the</strong> validity and usefulness <strong>of</strong> <strong>the</strong> output will be tested and through dialogs with
<strong>the</strong> users, <strong>the</strong> model design may be adjusted. The functionality <strong>of</strong> SAIA may also be improved
by incorporating o<strong>the</strong>r protected amphibian species with ecology similar to <strong>the</strong> Moor
frog, like for instance Crested newt (Triturus cristatus).
SAIA is not only a planning tool. The model can also be used to explore o<strong>the</strong>r aspects
<strong>of</strong> <strong>impact</strong> assessments or hypo<strong>the</strong>ses concerning road ecology. By applying a “virtual ecologist”
approach [96] different types <strong>of</strong> input data can be tested and compared. Of interest could
be how substituting counts <strong>of</strong> egg masses with presence/absence data or using aerial photos to
assess pond quality will affect model output. Additionally, virtual experiments with varying
sizes <strong>of</strong> <strong>the</strong> survey area could give insights about effective sampling schemes.
26

Synopsis
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32

CHAPTER ONE
EFFECTS OF WITHIN-PATCH
HETEROGENEITY ON CONNECTIVITY
IN POND-BREEDING AMPHIBIANS
STUDIED BY MEANS OF AN
INDIVIDUAL-BASED MODEL
Submitted to Web Ecology
October 2012
Under revision

Chapter One
Effects <strong>of</strong> within-patch heterogeneity on connectivity
in pond-breeding amphibians studied by means <strong>of</strong>
an individual-based model
M.-B. Pontoppidan and G. Nachman
Section for Ecology and Evolution, Department <strong>of</strong> Biology, University <strong>of</strong> Copenhagen
Universitetsparken 15, DK-2100 Copenhagen
Correspondence: M.-B. Pontoppidan (mbp@bio.ku.dk)
Abstract
The metapopulation framework presumes <strong>the</strong> habitat <strong>of</strong> a local population to be continuous
and homogenous, and patch area is <strong>of</strong>ten used as a proxy for population size. Many populations
<strong>of</strong> pond-breeding amphibians are assumed to follow metapopulations dynamics, and
connectivity is mostly measured between breeding ponds. However, <strong>the</strong> habitat <strong>of</strong> pondbreeding
amphibians is not only defined by <strong>the</strong> pond but, typically, consists <strong>of</strong> a breeding
pond surrounded by clusters <strong>of</strong> disjoint summer habitat patches interspersed with an agricultural/semi-urban
matrix. We hypo<strong>the</strong>size that <strong>the</strong> internal structure <strong>of</strong> a habitat patch may
change connectivity in two ways: i) by affecting animal movements and <strong>the</strong>reby emigration
and immigration probabilities; ii) by affecting habitat quality and population size. To test our
hypo<strong>the</strong>ses, we apply a spatially explicit individual-based model <strong>of</strong> Moor frog dispersal. We
find that <strong>the</strong> realised connectivity depends on internal structure <strong>of</strong> both <strong>the</strong> target and <strong>the</strong>
source patch as well as on how habitat quality is affected by patch structure. Although fragmentation
is generally thought to have negative effects on connectivity, our results suggest
that, depending on patch structure and habitat quality, positive effects on connectivity may
occur.
35

Chapter One
Introduction
Within <strong>the</strong> framework <strong>of</strong> metapopulations, inter-patch connectivity is modelled as an incidence
function measuring <strong>the</strong> dispersal success between two habitat patches (Moilanen and
Nieminen 2002). The essential components <strong>of</strong> <strong>the</strong> incidence function models are emigration
and immigration rates. The number <strong>of</strong> emigrating individuals is assumed to depend on <strong>the</strong>
population size <strong>of</strong> <strong>the</strong> donor patch and <strong>the</strong> probability <strong>of</strong> an individual actually leaving <strong>the</strong>
patch. Likewise, <strong>the</strong> number <strong>of</strong> immigrants depends on <strong>the</strong> probability that dispersing individuals
will find <strong>the</strong> target patch (Hanski and Simberl<strong>of</strong>f 1997; Moilanen and Hanski 2006;
Wiens 1997). A patch is assumed to constitute a continuous and homogenous habitat area
with all <strong>the</strong> necessary resources needed for <strong>the</strong> persistence <strong>of</strong> a local population. The incidence
function usually models <strong>the</strong> emigration and immigration rates as linear functions <strong>of</strong>
donor and target patch area, respectively. The survival probability during <strong>the</strong> transit between
two patches is modelled as a function <strong>of</strong> distance (Hanski and Simberl<strong>of</strong>f 1997; Kindlmann
and Burel 2008; Moilanen and Hanski 2001; Moilanen and Hanski 2006; Moilanen and
Nieminen 2002). However, it is questionable to what extent <strong>the</strong> above assumptions apply to
real populations <strong>of</strong> many species.
Regional populations <strong>of</strong> pond-breeding amphibians are frequently considered to be
structured as metapopulations (Hels 2002; Marsh 2008; Marsh and Trenham 2001; Smith and
Green 2005). Pond-breeding amphibians need ponds for breeding and development <strong>of</strong> tadpoles,
but o<strong>the</strong>rwise live most <strong>of</strong> <strong>the</strong>ir life in terrestrial habitat (also called summer habitat).
Proximity between <strong>the</strong> required habitat types (landscape complementation) is important for
population size and persistence (Dunning et al. 1992; Haynes et al. 2007; Johnson et al. 2007;
Pope et al. 2000). However, as a consequence <strong>of</strong> increased landscape fragmentation, <strong>the</strong>
summer habitat <strong>of</strong> many subpopulations does not form one continuous patch. Typically, a
subpopulation <strong>of</strong> pond-breeding amphibians occupies a landscape consisting <strong>of</strong> breeding
ponds surrounded by fragments <strong>of</strong> summer habitat interspersed with an agricultural/semiurban
matrix (Hamer and McDonnell 2008; Hartung 1991; Pillsbury and Miller 2008; Pope et
al. 2000; Sjögren-Gulve 1998; Tramontano 1998). Thus, <strong>the</strong> metapopulation premise <strong>of</strong> a
continuous and homogenous habitat patch is compromised, which might have consequences
for patch connectivity and <strong>the</strong> way it is measured (Ro<strong>the</strong>rmel 2004).
36

Chapter One
Numerous studies, empirical as well as modelling, have shown that structure and composition
<strong>of</strong> <strong>the</strong> habitat matrix can have strong effects on animal movement and dispersal success
(Bender and Fahrig 2005; Chin and Taylor 2009; Gustafson and Gardner 1996; Haynes
and Cronin 2006; Prevedello and Vieira 2010; Ricketts 2001; Vandermeer and Carvajal 2001;
Watling et al. 2011). Similar effects may be found within heterogeneous habitat patches, such
as those <strong>of</strong> pond-breeding amphibians. At <strong>the</strong> core <strong>of</strong> <strong>the</strong> habitat patch is <strong>the</strong> breeding pond
surrounded by satellites <strong>of</strong> summer habitat fragments separated by matrix habitat. The summer
habitat fragments within <strong>the</strong> habitat patch work as a collective, functioning as a filter
catching dispersers which will <strong>the</strong>n eventually find <strong>the</strong>ir way to <strong>the</strong> breeding pond. Emigration
and immigration probabilities may thus be influenced by <strong>the</strong> spatial distribution <strong>of</strong> <strong>the</strong>
summer habitat fragments within <strong>the</strong> habitat patch.
Metapopulation <strong>the</strong>ory usually assumes that <strong>the</strong> size <strong>of</strong> a subpopulation is proportional
to <strong>the</strong> area <strong>of</strong> <strong>the</strong> patch it inhabits. However, in some cases, <strong>the</strong> quality <strong>of</strong> <strong>the</strong> occupied habitat
may be a better predictor <strong>of</strong> patch carrying capacity (Jaquiéry et al. 2008; Moilanen and Hanski
1998). One <strong>of</strong> <strong>the</strong> factors that may affect habitat quality is <strong>the</strong> degree <strong>of</strong> habitat fragmentation.
Thus, a fragmented habitat may not be able to sustain as large a population as a nonfragmented
habitat <strong>of</strong> equal area due to a combination <strong>of</strong> negative edge effects and reduced
landscape complementation (Dunning et al. 1992; Haynes et al. 2007; Johnson et al. 2007;
Lehtinen et al. 2003; Pope et al. 2000; Ries et al. 2004).
The internal structure <strong>of</strong> a habitat patch may <strong>the</strong>refore change inter-patch connectivity
in two ways: i) by affecting animal movements and <strong>the</strong>reby emigration and immigration probabilities;
ii) by affecting habitat quality and population size. To test how intra-patch structuring
may influence dispersal success and connectivity we apply a spatially explicit individualbased
model <strong>of</strong> how <strong>the</strong> Moor frog (Rana arvalis Nilsson) moves in a heterogeneous landscape.
The model is part <strong>of</strong> a larger study aiming at modelling <strong>the</strong> effect <strong>of</strong> <strong>roads</strong> on regional
persistence <strong>of</strong> Moor frog metapopulations (Pontoppidan and Nachman in prep.). With this
model, we test <strong>the</strong> following
Does <strong>the</strong> distance between <strong>the</strong> breeding pond and <strong>the</strong> summer habitat within a habitat
patch affect inter-patch connectivity
Does <strong>the</strong> degree <strong>of</strong> summer habitat fragmentation within a habitat patch affect inter-patch
connectivity
37

Chapter One
Do effects <strong>of</strong> pond distance and summer habitat fragmentation on inter-patch connectivity
interact
Does <strong>the</strong> quality <strong>of</strong> <strong>the</strong> habitat patch affect inter-patch connectivity
Methods
Model species
Long distance dispersal in Moor frogs takes place predominantly during <strong>the</strong> juvenile lifestage.
Shortly after metamorphosis, <strong>the</strong> young frogs leave <strong>the</strong> natal pond and disperse into <strong>the</strong>
surrounding landscape seeking out suitable summer habitat. Dispersal distances are between a
few hundred meters up to 1-2 kilometres (Baker and Halliday 1999; Hartung 1991; Sinsch
2006; Vos and Chardon 1998). The juveniles stay in terrestrial habitat 2-3 years until <strong>the</strong>y
reach maturity. During early spring, <strong>the</strong> adults move to <strong>the</strong> breeding ponds. Soon after breeding,
<strong>the</strong> frogs return to <strong>the</strong> summer habitat, which lies mostly within a 400 m radius from <strong>the</strong>
breeding pond Adult frogs show a high degree <strong>of</strong> site fidelity and <strong>of</strong>ten use <strong>the</strong> same breeding
pond and summer habitat patch from year to year (Hartung 1991; Loman 1984, 1994; Semlitsch
2008; Tramontano 1998).
Model overview
The model considers nine subpopulations <strong>of</strong> Moor frogs within a spatially explicit landscape
matrix. Each landscape cell represents an area <strong>of</strong> 10 x 10 meters, which can be ei<strong>the</strong>r summer
habitat or matrix habitat. Each habitat type is associated with a daily survival probability (s)
and an index <strong>of</strong> attractiveness (a) (table 1). The area inhabited by a subpopulation is defined
by <strong>the</strong> habitat patch, which comprises a breeding pond, all <strong>the</strong> summer habitat fragments located
within migration distance from <strong>the</strong> pond as well as <strong>the</strong> intermediate matrix habitat (Fig.
1).
The model simulations mimic <strong>the</strong> dispersal <strong>of</strong> juvenile Moor frogs. Successful dispersal
requires two events: 1) movement <strong>of</strong> a juvenile frog to summer habitat outside its natal habitat
patch and 2) subsequent movement from <strong>the</strong> new summer habitat to a nearby breeding pond.
In real life dispersal starts just after metamorphosis in early summer and lasts until hibernation
in <strong>the</strong> autumn. The second part <strong>of</strong> <strong>the</strong> dispersal event takes place in <strong>the</strong> spring 2.5 years
later. For simplicity, we simulate <strong>the</strong> two events, as if <strong>the</strong>y take place in <strong>the</strong> same year.
38

Chapter One
At <strong>the</strong> start <strong>of</strong> a simulation, 500 frogs are created at each breeding pond. Each individual
has an inherent random direction, which characterizes its preferred direction <strong>of</strong> movement.
This direction does not change unless summer habitat is found. At each time step, frogs move
to one <strong>of</strong> its n neighbouring cells according to <strong>the</strong> following movement rules: A frog has a
sensing area <strong>of</strong> 225 degrees placed symmetrically around its preferred direction and within
this area it moves to cell i with a probability that depends on <strong>the</strong> cell’s attractiveness (a i ). The
probability <strong>of</strong> moving into cell i is calculated as
∑
where ∑ is <strong>the</strong> total attractiveness
<strong>of</strong> <strong>the</strong> n cells located within <strong>the</strong> sensing area. A uniform pseudorandom number is
selected to choose <strong>the</strong> cell to move to. Once a cell is chosen, <strong>the</strong> frog moves to a random position
within <strong>the</strong> cell. The movement rules generate a biased random walk away from <strong>the</strong> natal
pond and in <strong>the</strong> preferred direction.
The time step <strong>of</strong> <strong>the</strong> model is one day and <strong>the</strong> simulated period is 120 days. Dispersal
continues until <strong>the</strong> frog ei<strong>the</strong>r settles, dies or <strong>the</strong> time runs out. Frogs encountering a cell with
summer habitat randomly choose whe<strong>the</strong>r to settle in <strong>the</strong> cell or not. Settled frogs stay in <strong>the</strong>
summer habitat until day 75. Hereafter, <strong>the</strong>y start moving towards <strong>the</strong> breeding pond associated
with <strong>the</strong> habitat patch in which <strong>the</strong>y have spent <strong>the</strong> summer. For each day, <strong>the</strong> survival
probability <strong>of</strong> every frog is based on <strong>the</strong> daily survival rate associated with <strong>the</strong> habitat type it
occupies. Netlogo (Wilensky 1999) is used as modelling environment (freely downloadable at
http://ccl.northwestern.edu/netlogo). Full model documentation following <strong>the</strong> ODD-template
suggested by Grimm et al. (2006; 2010) is found in supplementary material, Appendix A.
Scenarios
A landscape consisting <strong>of</strong> 300x300 cells is constructed as a torus with nine evenly spaced
habitat patches. We define <strong>the</strong> habitat patch <strong>of</strong> a subpopulation as a complementary habitat
patch containing not only <strong>the</strong> breeding pond but also all summer habitat fragments within 400
m from <strong>the</strong> pond. Five habitat patches are configured with one coherent summer habitat fragment
randomly placed in a distance <strong>of</strong> 100 meters from <strong>the</strong> pond. These habitat patches serve
as control patches as <strong>the</strong>y have non-fragmented summer habitat and high landscape complementation.
The remaining four habitat patches are test patches, in which <strong>the</strong> number <strong>of</strong> summer
habitat fragments and <strong>the</strong>ir distance to <strong>the</strong> breeding pond are determined by <strong>the</strong> chosen
parameter values for <strong>the</strong> number <strong>of</strong> fragments (P) and distance to <strong>the</strong> pond (d) (fig. 1, table 1).
In each <strong>of</strong> <strong>the</strong> nine habitat patches <strong>the</strong> total area <strong>of</strong> <strong>the</strong> summer habitat sums to 0.81 ha (81
39

Chapter One
cells) irrespective <strong>of</strong> fragmentation. The same set <strong>of</strong> parameter values is applied to all test
patches in a given landscape scenario. We run 100 simulations for every combination <strong>of</strong> <strong>the</strong>
parameter values for P and d given in table 1. For each <strong>of</strong> <strong>the</strong> 100 simulations, <strong>the</strong> position <strong>of</strong>
<strong>the</strong> test and control patches is randomly shuffled. At <strong>the</strong> end <strong>of</strong> each simulation we record <strong>the</strong>
number <strong>of</strong> dispersers that has settled at each breeding pond, and <strong>the</strong> origin <strong>of</strong> <strong>the</strong> dispersers
(i.e. <strong>the</strong>ir natal pond).
Connectivity
In metapopulation ecology, most measures <strong>of</strong> connectivity between patch i and j are based on
<strong>the</strong> formula:
,
where j is <strong>the</strong> source patch and i <strong>the</strong> target patch. A i and A j denote <strong>the</strong> area <strong>of</strong> patch i and j,
respectively, and b and c are parameters scaling patch area to emigration and immigration
rates, respectively. D(d ij , α) is a species-specific function describing <strong>the</strong> dispersal ability <strong>of</strong>
<strong>the</strong> species (Kindlmann and Burel 2008; Moilanen and Hanski 2001; Moilanen and Nieminen
2002). In this study we substitute <strong>the</strong> dispersal parameter D(d ij , α) with <strong>the</strong> actual dispersal
success between patches obtained by <strong>the</strong> individual-based simulations and compute connectivity
as:
(1)
where p ij is <strong>the</strong> probability <strong>of</strong> a disperser getting from habitat patch j to habitat patch i. A j and
A i are <strong>the</strong> total area <strong>of</strong> summer habitat fragments within <strong>the</strong> two habitat patches.
Fragmentation <strong>of</strong> summer habitat within <strong>the</strong> habitat patch is expected to have a negative
effect on <strong>the</strong> quality <strong>of</strong> habitat patch so that a habitat patch with highly fragmented summer
habitat supports fewer individuals even though <strong>the</strong> total area is <strong>the</strong> same (Fahrig 2003). To
compensate for <strong>the</strong> effect <strong>of</strong> summer habitat fragmentation on <strong>the</strong> quality <strong>of</strong> <strong>the</strong> habitat patch
we introduce a quality-weighted connectivity measure (Moilanen and Hanski 1998):
′ 2
where Q denotes <strong>the</strong> quality <strong>of</strong> <strong>the</strong> habitat patch. In principle, Q corresponds to A in eq. 1, but
only if patch quality is independent <strong>of</strong> fragmentation <strong>of</strong> summer habitat within <strong>the</strong> habitat
40

Chapter One
patch. If this is not <strong>the</strong> case, Q is computed as <strong>the</strong> total area <strong>of</strong> summer habitat fragments
within <strong>the</strong> habitat patch weighted by <strong>the</strong> degree <strong>of</strong> fragmentation (Jaeger 2000):
∑
/ , z 0 3
where P is <strong>the</strong> number <strong>of</strong> summer habitat fragments in habitat patch i; A k is <strong>the</strong> area <strong>of</strong> <strong>the</strong> k th
fragment <strong>of</strong> summer habitat, and z is a scaling factor indicating <strong>the</strong> effect <strong>of</strong> fragmentation on
quality. If z = 1 <strong>the</strong>n Q i = A i ; if k > 1 and z > 1 <strong>the</strong>n Q i < A i and if k > 1 and 0 < z < 1 <strong>the</strong>n Q i >
A i .
In order to evaluate <strong>the</strong> effects <strong>of</strong> fragmentation and pond distance on connectedness at
<strong>the</strong> landscape level we compute mean connectivity <strong>of</strong> <strong>the</strong> test patches as (Goodwin and Fahrig
2002; Kindlmann and Burel 2008):
̅
∑ ∑
i j
4
where n t is <strong>the</strong> number <strong>of</strong> test patches (4). In all simulations, <strong>the</strong> structure within <strong>the</strong> control
patches is <strong>the</strong> same and <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> control patches to <strong>the</strong> connectivity measure
remains constant. This allows us to distinguish between <strong>the</strong> effect <strong>of</strong> structure within source
and target patches on connectivity:
Mean connectivity from control to test patches. Evaluates <strong>the</strong> effect <strong>of</strong> pond distance and
fragmentation within <strong>the</strong> target habitat patch on connectivity
̅
∑ ∑
where n c is <strong>the</strong> number <strong>of</strong> control patches.
Mean connectivity from test to control patches. Evaluates <strong>the</strong> effect <strong>of</strong> pond distance and
fragmentation within <strong>the</strong> source patch on connectivity. It is computed as
̅
∑
∑
We compute ̅,̅ and ̅ for each scenario and average <strong>the</strong>m across replicates.
stcendfrmentiwiintdonocstcnvity. tisoutMean connectivity
values adjusted for quality are denoted ′ , ′ and ′ , respectively, and are computed
by replacing A with Q in <strong>the</strong> above equations. We combine habitat patch fragmentation
(P) with pond distance (d) in a fully factorial design, using <strong>the</strong> following values <strong>of</strong> P = 4 and
9 and <strong>of</strong> d = 100, 200 and 300. For each <strong>of</strong> <strong>the</strong> six combinations <strong>of</strong> P and d, we construct a
41

Chapter One
series <strong>of</strong> ′ and ′ with z-values ranging from 0.7 to 2.0. We transform <strong>the</strong> ′ values into a
relative connectivity value (R) by dividing with <strong>the</strong> corresponding mean connectivity found
when P = 1 and d = 100, i.e. R = ′ (P,d) / ′ (P=1, d=100). For any given combination <strong>of</strong>
pond distance and habitat fragmentation, this value expresses <strong>the</strong> relative effect habitat quality
has on mean connectivity.
We use a two-way ANOVA to test for <strong>the</strong> effect <strong>of</strong> <strong>the</strong> number <strong>of</strong> summer habitat fragments
within <strong>the</strong> habitat patch and <strong>the</strong>ir distance to <strong>the</strong> breeding pond on mean connectivity
values. We also use an ANOVA to test for effects <strong>of</strong> patch structure on <strong>the</strong> proportion <strong>of</strong> juveniles
settling in <strong>the</strong>ir natal patch.
Results
Mean connectivity between test patches is clearly affected by <strong>the</strong> structure <strong>of</strong> <strong>the</strong> habitat
patches, showing strong interactions between pond distance and fragmentation (F 8,891 = 37.5,
p < 0.0001) (fig. 2a, table 2a). Pond distance has a positive effect on <strong>the</strong> connectivity between
highly fragmented habitat patches, while <strong>the</strong> effect is <strong>the</strong> opposite between non-fragmented
patches. Moreover, fragmentation <strong>of</strong> habitat patches has a positive effect on connectivity, especially
between habitat patches with long pond distance. Intra-patch structure also affects <strong>the</strong>
number <strong>of</strong> juveniles being intercepted by summer habitat within <strong>the</strong> natal habitat patch and,
thus, prevented from dispersing. The probability <strong>of</strong> staying in <strong>the</strong> home patch increases with
fragmentation and decreases with distance (F 8,891 = 19196, p < 0.0001) (fig. 2b, table 2d).
Distinguishing between outward and inward movements between test and control
patches enables us to tease apart <strong>the</strong> effects target and source patch structure, respectively,
have on connectivity. Mean connectivity from test to control patches shows that decreasing
fragmentation and increasing pond distance within source patches promotes connectivity
(F 8,891 = 58.1, p < 0.0001). The highest connectivity is found in non-fragmented source
patches with long pond distance. Lowest connectivity is found in fragmented source patches
with short pond distance (fig. 3a, table 2b). Mean connectivity from control to test patches
reveals target patch structure to have an opposite effect on connectivity. Fragmentation <strong>of</strong>
summer habitat in <strong>the</strong> target patches promotes connectivity while distance between breeding
pond and summer habitat has a negative effect (F 8,891 = 154.5, p < 0.0001) (fig. 3b, table 2c).
42

Chapter One
The relative effect <strong>of</strong> habitat quality on mean connectivity (R) will decrease with increasing
z-values. When R > 1, <strong>the</strong> quality-weighted connectivity for a given scenario is
greater than <strong>the</strong> mean connectivity in a non-fragmented habitat patch with high landscape
complementation (i.e. P = 1, d = 100 m). At R-values below 1 <strong>the</strong> effect <strong>of</strong> habitat patch structure
reduces connectivity compared to <strong>the</strong> control habitat patches. The threshold z-values at
which R shifts below 1 depends on patch structure. In less fragmented target patches threshold-values
range from 1 – 1.6 as pond distance decreases. Target patches with nine fragments
exhibit a much narrower range <strong>of</strong> thresholds with z-values between 1.2 and 1.4 (fig. 4a). Connectivity
is negatively affected by fragmentation in source patches, which again is reflected in
<strong>the</strong> z-thresholds (fig. 4b). Here most thresholds are less than 1, indicating that <strong>the</strong> negative
effect <strong>of</strong> patch structure on connectivity only can be counterbalanced if fragmentation has a
positive effect on habitat quality.
Discussion
Inter-patch distance is widely recognised as a key factor for dispersal success (Goodwin and
Fahrig 2002; Gustafson and Gardner 1996; Hanski 1998; Prevedello and Vieira 2010). All
else being equal, increasing inter-patch distances means more time spent in inhospitable matrix
habitat, with consequently higher mortality rates. In our model, <strong>the</strong> setup ensures equal
inter-pond distances, thus, if no o<strong>the</strong>r factors interfered we would expect dispersal success to
be <strong>the</strong> same between all pond pairs. Our results show that this is not <strong>the</strong> case; dispersal success
varies depending on <strong>the</strong> structure <strong>of</strong> <strong>the</strong> habitat patches. The distribution <strong>of</strong> summer habitat
fragments within source as well as target patches is important for emigration and immigration
probabilities.
Emigration probability depends on <strong>the</strong> chances <strong>of</strong> not being retained by summer habitat
within <strong>the</strong> home (habitat) patch. This probability increases <strong>the</strong> fur<strong>the</strong>r away from <strong>the</strong> breeding
pond <strong>the</strong> summer habitat is found and decreases <strong>the</strong> more fragmented <strong>the</strong> summer habitat is.
Conversely, <strong>the</strong> proportion <strong>of</strong> juveniles that are retained and thus return to <strong>the</strong>ir natal pond
increases with fragmentation <strong>of</strong> summer habitat and decreases with pond distance. The opposite
pattern is found when looking at immigration, i.e. <strong>the</strong> probability <strong>of</strong> a dispersing juvenile
finding summer habitat in a new patch. Immigration probability increases with fragmentation
<strong>of</strong> summer habitat but decreases with pond distance. Thus, <strong>the</strong> combination <strong>of</strong> effects creates
43

Chapter One
a complex pattern <strong>of</strong> dispersal success, depending on <strong>the</strong> structure <strong>of</strong> source and target
patches.
Bowman et al. (2002) suggest that for non-searching dispersers, immigration probability
will be proportional to <strong>the</strong> linear dimensions <strong>of</strong> <strong>the</strong> target patch. In a simulation study, Pfenning
et al. (2004) found immigration rate to increase with perimeter-to-area ratio; dispersers
using correlated (straight) walk having <strong>the</strong> strongest effect. The dispersal patterns found in
this study can be explained by similar statistical reasoning. As fragmentation <strong>of</strong> summer habitat
increases, <strong>the</strong> perimeter:area ratio <strong>of</strong> summer habitat fragments also increases. In this
study, <strong>the</strong> linear dimension <strong>of</strong> summer habitat fragments increases from ca 100 meters to ca
270 meters as <strong>the</strong> summer habitat gets more fragmented. Increasing pond distance causes <strong>the</strong>
gabs between <strong>the</strong> summer habitat fragments to become wider. Consequently, <strong>the</strong> probability
<strong>of</strong> dispersers encountering summer habitat becomes relatively smaller as pond distance increases.
The effects <strong>of</strong> <strong>the</strong> p:a ratio and gab size will interact. At any given pond distance, <strong>the</strong>
probability <strong>of</strong> finding summer habitat patches will be proportional to <strong>the</strong> ratio between <strong>the</strong>
linear dimension <strong>of</strong> summer habitat patches and gabs. This is <strong>the</strong> same whe<strong>the</strong>r <strong>the</strong> movement
is outbound or inbound. Successful dispersal will depend on <strong>the</strong> probability <strong>of</strong> a disperser to
avoid summer habitat within <strong>the</strong> home patch and <strong>the</strong> probability <strong>of</strong> finding summer habitat in
<strong>the</strong> target patch.
Exchange <strong>of</strong> individuals between habitat patches is important for <strong>the</strong> persistence <strong>of</strong> a
regional population <strong>of</strong> pond-breeding amphibians (Marsh and Trenham 2001). Our results
suggest that fragmentation <strong>of</strong> summer habitat within target habitat patches can have positive
effects on dispersal success. However, intra-patch structure may also affect <strong>the</strong> persistence <strong>of</strong>
<strong>the</strong> local population; habitat fragmentation is in general thought to have a negative effect on
habitat quality (Jaeger 2000; Pillsbury and Miller 2008; Vos and Chardon 1998). The same
spatial distribution that promotes regional persistence, thus, seems to impair local persistence.
The results suggest that adjusting connectivity for <strong>the</strong> effect <strong>of</strong> fragmentation on target quality
may <strong>of</strong>fset <strong>the</strong> positive effects <strong>of</strong> fragmentation on dispersal success. This, however, will depend
on how strongly fragmentation is assumed to affect habitat quality (i.e. <strong>the</strong> z-value) and
<strong>the</strong> structure <strong>of</strong> <strong>the</strong> target patch. We find that <strong>the</strong> threshold values in target patches very much
depend on patch structure. For some landscapes a downscaling <strong>of</strong> effective area to 0.48 ha is
needed before positive effects are turned into negative. In source patches fragmentation reduces
connectivity and this pattern is not changed when adjusting for habitat quality, unless
44

Chapter One
we assume positive quality effects <strong>of</strong> fragmentation and up-scale effective area to 2 ha. Our
simulations also reveal an increase in dispersers settling in <strong>the</strong>ir natal patch as <strong>the</strong> habitat gets
more fragmented. This will benefit <strong>the</strong> local population by increasing <strong>the</strong> population size.
Thus, <strong>the</strong> negative effects fragmentation can have on habitat quality may be reduced by an
increased recruitment <strong>of</strong> juvenile frogs.
Like fragmentation, pond distance may affect habitat quality. In <strong>the</strong> breeding season,
mature frogs move between <strong>the</strong> summer habitat and <strong>the</strong> breeding pond. Thus, longer distances
through <strong>the</strong> matrix may induce higher mortality. Fur<strong>the</strong>rmore, breeding ponds with high quality
summer habitat in <strong>the</strong> immediate surroundings tend to have higher juvenile survival and
thus more dispersers (Hamer and McDonnell 2008; Puglis and Boone 2012; Todd and
Ro<strong>the</strong>rmel 2006). For <strong>the</strong> sake <strong>of</strong> simplicity, we have chosen not to incorporate <strong>the</strong>se effects
into <strong>the</strong> quality-weighted connectivity measure. We expect, though, that <strong>the</strong> negative effect a
long pond distance will have on local population size, at least partly, will negate <strong>the</strong> positive
effect on dispersal success.
Conclusion
To our knowledge, this is <strong>the</strong> first study looking at <strong>the</strong> effect <strong>of</strong> intra-patch structure on connectivity.
We find that <strong>the</strong> realised connectivity depends on internal structure <strong>of</strong> both <strong>the</strong> target
and <strong>the</strong> source patch as well as on how habitat quality is affected by patch structure. Although
fragmentation is generally thought to have negative effects on connectivity, our results
suggest that, depending on patch structure and habitat quality, positive effects on connectivity
may occur. Connectivity is frequently used in conservation planning and studies on pond
breeding amphibian <strong>of</strong>ten use distance between breeding ponds as a measure <strong>of</strong> dispersal ability.
This study emphasises that complex interactions between individuals and landscape elements
in both source and target patches determine <strong>the</strong> connectivity between habitat patches.
Acknowledgments
This study is part <strong>of</strong> a PhD-project funded by <strong>the</strong> Danish Road Directorate. We thank Uta
Berger and Volker Grimm for valuable comments on <strong>the</strong> model ODD.
45

Chapter One
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48

Chapter One
Tables
Table 1 Default settings <strong>of</strong> parameters and <strong>the</strong> range <strong>of</strong> parameter values used in <strong>the</strong> simulations
Parameter Description Default Test values
z
Effect <strong>of</strong> summer habitat fragmentation
on habitat quality
1 0.7 – 2.0
A Area <strong>of</strong> summer habitat 0.81 ha (81 cells )
d
Distance between pond and
summer habitat
100m (10 cells)
100, 200, 300 m
P
a
s
Number <strong>of</strong> summer habitat
fragments
Weight <strong>of</strong> habitat type on direction
Daily survival
1 1, 4, 9
Matrix = 1
Summer habitat = 2
Matrix = 0.985
Summer habitat = 0.995
49

Chapter One
Table 2 Anova test results. Effect <strong>of</strong> pond distance (d) and number <strong>of</strong> summer habitat fragments
(P) on mean connectivity ̅ , ̅,̅ and <strong>the</strong> proportion <strong>of</strong> non-dispersing juveniles (1)
Source df Model a Model b Model c Model d
F p F p F p F p
d 2 36.9 < 0.0001 5.1 0.0004 3.6 0.006 49871.7 < 0.0001
P 2 6.7 0.0013 107.2 < 0.0001 160.9 < 0.0001 20113.4 < 0.0001
P*d 4 69.4 < 0.0001 115.1 < 0.0001 449.7 < 0.0001 3399.4 < 0.0001
(1) Model a evaluates <strong>the</strong> overall effect <strong>of</strong> patch structure while model b and c analyses <strong>the</strong>
effect <strong>of</strong> source patch structure and target patch structure, respectively. Model d tests <strong>the</strong> effect
<strong>of</strong> source patch structure on <strong>the</strong> proportion <strong>of</strong> dispersing juveniles settling in <strong>the</strong>ir natal
habitat patch.
50

Chapter One
Figure legends
Figure 1:
Model landscape with nine habitat patches. Each habitat patch is defined by a central breeding
pond (black dot), fragments <strong>of</strong> summer habitat (dark grey shapes) and matrix (light gray)
within <strong>the</strong> habitat patch boundary. The model landscape contains five control (habitat) patches
and four test (habitat) patches (see text). Distance between breeding pond and summer habitat
is denoted d.
Figure 2:
Effect <strong>of</strong> habitat patch structure on a) mean connectivity between test patches, b) proportion
<strong>of</strong> dispersing juveniles settling in <strong>the</strong>ir natal habitat patch.
Figure 3:
Effect <strong>of</strong> (a) target patch structure and (b) source patch structure on mean connectivity between
habitat patches serving as test and control patches, respectively.
Figure 4:
Relative effect <strong>of</strong> habitat quality on mean connectivity (R) in a) target patches and b) source
patches for different landscape scenarios. At a z-value equal to 1 (dotted, vertical line), <strong>the</strong>
effective area equals <strong>the</strong> real area. R-values along this line represent <strong>the</strong> relative effect a particular
patch structure has on mean connectivity. When R = 1 (dashed, horizontal line), <strong>the</strong>
quality weighted connectivity for a given landscape corresponds to <strong>the</strong> mean connectivity
between habitat patches serving as control patches (i.e. scenario with P = 1, d = 100). The z-
value <strong>of</strong> <strong>the</strong> intercept between <strong>the</strong> dashed line and a given curve can be interpreted as <strong>the</strong>
threshold at which <strong>the</strong> habitat quality is low enough to shift a positive effect on connectivity
into a negative effect.
51

Chapter One
Figures
Figure 1
52

Chapter One
Figure 2
(a)
(b)
Figure 3
(a) Target patch
(b) Source patch
53

Chapter One
Figure 4
(a) Target patch
(b) Source patch
54

Chapter One
Supplementary material - Appendix A
Model ODD
1. Purpose
The purpose <strong>of</strong> <strong>the</strong> model is to analyse <strong>the</strong> effect <strong>of</strong> intra-patch structure on inter-patch dispersal
success and connectivity.
2. Entities, state variables, and scales
Breeding ponds are treated as stationary agents. Each pond is characterized by a unique idnumber,
<strong>the</strong> habitat patch type (test or control patch) and <strong>the</strong> quality-weighted area <strong>of</strong> associated
summer habitat. Frog-agents are characterized by <strong>the</strong> pond in which <strong>the</strong>y are hatched and
<strong>the</strong> breeding pond <strong>the</strong>y immigrate to. The extent <strong>of</strong> <strong>the</strong> model landscape is 300 x 300 grid
cells, and each grid cell represents 10 x 10 m. Grid cells belong ei<strong>the</strong>r to Matrix habitat or
Summer habitat. Each habitat type is associated with a habitat-attraction (indicating how willing
frogs will be to enter <strong>the</strong> habitat) and <strong>the</strong> frogs’ daily survival probability in <strong>the</strong> habitat.
The simulation runs for 120 time steps, each representing one day.
3. Process overview and scheduling
500 Frog-agents are located at each <strong>of</strong> <strong>the</strong> Pond-agents. During each time-step <strong>the</strong> following
procedures are executed: Settle (evaluates if a Frog-agent stops dispersing), Move (movement
<strong>of</strong> dispersing Frog-agents), Homing (movement <strong>of</strong> settled Frog-agents towards breeding
pond) and Survival (evaluates if a Frog-agent survives). The simulation stops at time step 120
and <strong>the</strong> procedure Connectivity is run, computing dispersal rates and connectivity.
4. Design concepts
Emergence
Immigration rates will emerge as a response to <strong>the</strong> landscape configuration.
Adaptation & Objectives
To avoid desiccation and <strong>the</strong>reby increase survival Frog-agents are assumed to move in response
<strong>the</strong> moistness <strong>of</strong> its surroundings. The moister, in general, a habitat is <strong>the</strong> more attractive
<strong>the</strong> habitat is for <strong>the</strong> frog as indicated by <strong>the</strong> habitat-attraction parameter a. Dispersing
juvenile Moor frogs have an innate tendency to move away from <strong>the</strong>ir natal pond. In <strong>the</strong> simu-
55

Chapter One
lation <strong>the</strong> movement <strong>of</strong> <strong>the</strong> Frog-agents is thus oriented in a random direction away from <strong>the</strong>
pond, and <strong>the</strong>y are not allowed to backtrack.
Sensing
Frog-agents are assumed to be aware <strong>of</strong> <strong>the</strong>ir own state-variables. Frog-agents are also aware
<strong>of</strong> <strong>the</strong> habitat-attraction <strong>of</strong> <strong>the</strong> grid cells, as well as <strong>the</strong> identity <strong>of</strong> <strong>the</strong> ponds.
Interaction
There is no interaction between frog-agents. Movement decisions <strong>of</strong> <strong>the</strong> Frog-agents depend
on <strong>the</strong> habitat type <strong>of</strong> <strong>the</strong> neighbouring cells. Survival <strong>of</strong> <strong>the</strong> Frog-agents depends on <strong>the</strong> daily
survival rates <strong>of</strong> <strong>the</strong> traversed habitat.
Stochasticity
Which cell to move to is chosen randomly from neighbouring cells with <strong>the</strong> probability <strong>of</strong>
being chosen weighted by <strong>the</strong> habitat-attraction and <strong>the</strong> number <strong>of</strong> neighbouring cells with <strong>the</strong>
same value. If Frog-agents occupy a cell with summer habitat <strong>the</strong>y will stop dispersing with a
certain probability. The probability increases with time.
Observation
At <strong>the</strong> end <strong>of</strong> each run <strong>the</strong> number <strong>of</strong> dispersers settled at each breeding pond and <strong>the</strong>ir natalpond
is registered and <strong>the</strong> following are calculated (see also Method-section in main text):
Mean connectivity between test patches
Mean connectivity from control to test patches
Mean connectivity from test to control patches
Proportion <strong>of</strong> dispersers settled in home habitat patch
5. Initialization
Nine habitat patches are constructed according to <strong>the</strong> test scheme (see Method section in main
text). Map-scan procedure is run calculating <strong>the</strong> weighted area <strong>of</strong> summer habitat in each
habitat patch. 500 Frog-agents are located on each pond-agent, <strong>the</strong>ir direction set randomly.
6. Input data
No input data are used
56

Chapter One
7. Submodels
Map-scan
The procedure delimits individual summer habitat fragments within <strong>the</strong> habitat patch and
computes <strong>the</strong> effective (quality-weighted) area <strong>of</strong> summer habitat. Interconnected summer
habitat cells define an individual summer habitat fragment. The area (A) <strong>of</strong> each summer habitat
fragment is calculated as <strong>the</strong> sum <strong>of</strong> cells within <strong>the</strong> patch. The effective area <strong>of</strong> summer
habitat is, subsequently, calculated as ∑
/ where A k is <strong>the</strong> area <strong>of</strong> <strong>the</strong> k th summer
habitat fragment, P <strong>the</strong> number <strong>of</strong> summer habitat fragments within <strong>the</strong> habitat patch, and
z a constant weighting <strong>the</strong> effect <strong>of</strong> fragmentation on habitat quality (z > 0).
Settle
Dispersing frogs occupying a summer habitat cell has a certain probability <strong>of</strong> settling and
cease moving. The initial settling probability is 0, increasing every time step with 0.04 and
ending at 0.96.
Move
Assuming <strong>the</strong> frog to head in <strong>the</strong> direction it was assigned when it left <strong>the</strong> natal pond, a frog
can move to one <strong>of</strong> its neighbouring cells located within ±110 0 from <strong>the</strong> preferred direction.
Based on <strong>the</strong> habitat-attraction <strong>of</strong> <strong>the</strong> neighbouring cells frogs decide which cell-type <strong>the</strong>y
want to move to. The probability <strong>of</strong> moving into cell i is a function <strong>of</strong> habitat attraction (a) <strong>of</strong>
<strong>the</strong> accessible neighbouring cells (n):
∑
. A uniform pseudorandom number is selected
to choose <strong>the</strong> cell to move to. Once a cell is chosen <strong>the</strong> frog moves to a random position
within <strong>the</strong> cell. The direction <strong>of</strong> <strong>the</strong> frogs does not change.
Homing
After time step 75 settled frogs have <strong>the</strong>ir direction set towards <strong>the</strong>ir breeding pond and <strong>the</strong>y
start moving again following <strong>the</strong> Move-procedure. If <strong>the</strong>y get within a distance <strong>of</strong> 2 cells from
<strong>the</strong> breeding pond, <strong>the</strong> frogs move directly to <strong>the</strong> breeding pond and stay <strong>the</strong>re.
Survival
For each frog a pseudo-random number is drawn between 0 and 1. If <strong>the</strong> number exceeds <strong>the</strong>
daily survival probability <strong>of</strong> <strong>the</strong> frog’s current cell, <strong>the</strong> frog dies.
57

Chapter One
Connectivity
At <strong>the</strong> end <strong>of</strong> each simulation, dispersal probabilities are computed for all pair wise combinations
<strong>of</strong> habitat patches and connectivity measures are computed as described in <strong>the</strong> method
section.
58

CHAPTER TWO
CHANGES IN BEHAVIOURAL RESPONSES
TO INFRASTRUCTURE AFFECTS LOCAL
AND REGIONAL CONNECTIVITY —
A SIMULATION STUDY ON POND BREEDING
AMPHIBIANS
Submitted to Nature Conservation
December 2012

Chapter Two
Changes in behavioural responses to infrastructure
affects local and regional connectivity — a simulation
study on pond breeding amphibians
Maj-Britt Pontoppidan, Gösta Nachman
Section for Ecology and Evolution
Department <strong>of</strong> Biology
University <strong>of</strong> Copenhagen
Universitetsparken 15
DK-2100 Copenhagen
Corresponding author:
M-B. Pontoppidan
email: mbp@bio.ku.dk
phone: +45 51518791
61

Chapter Two
Abstract
An extensive and expanding infrastructural network destroys and fragments natural habitat
and has detrimental effect on abundance and population viability <strong>of</strong> many amphibian species.
Roads functions as barriers in <strong>the</strong> landscape. They separate local populations from each o<strong>the</strong>r
or prevent access to necessary resources. Therefore, road density and traffic intensity in a region
may have severe <strong>impact</strong> on regional as well as local connectivity. Amphibians may be
able to detect and avoid unsuitable habitat. Individuals’ ability to avoid <strong>roads</strong> can reduce road
mortality but at <strong>the</strong> same time road avoidance behaviour, can increase <strong>the</strong> barrier effect <strong>of</strong> <strong>the</strong>
road and reduce connectivity. We use an individual based model to explore how changes in
road mortality and road avoidance behaviour affect local and regional connectivity in a population
<strong>of</strong> Moor frogs (Rana arvalis). The results indicate that road mortality has a strong negative
effect on regional connectivity, but only a small effect on local connectivity. Regional
connectivity is positively affected by road avoidance and <strong>the</strong> effect becomes more pronounced
as road mortality decreases. Road avoidance also has a positive effect on local connectivity.
When road avoidance is total and <strong>the</strong> road functions as a 100% barrier regional
connectivity is close to zero, while local connectivity exhibit very elevated values. The results
suggest that <strong>roads</strong> may affect not only regional or metapopulation dynamics but also have a
direct effect on local population dynamics.
62

Chapter Two
Introduction
All over <strong>the</strong> world, amphibian populations are declining and many amphibian species are
listed in <strong>the</strong> IUCN as threatened or vulnerable (IUCN 2012). The causes for <strong>the</strong> decline are
hypo<strong>the</strong>sized to be (combinations <strong>of</strong>) factors such as climate change, diseases, predation and
UV-radiation. But <strong>the</strong> main factor, especially in <strong>the</strong> western world, is thought to be <strong>the</strong> increasing
urbanisation (Alford and Richards 1999; Beebee and Griffiths 2005; Collins and
Storfer 2003; Gardner et al. 2007). The negative effect <strong>of</strong> urbanisation is not only due to
changes in land use and destruction <strong>of</strong> habitat. A huge infrastructural network functions as
barriers to movement and causes <strong>the</strong> death <strong>of</strong> a huge number <strong>of</strong> amphibians every year (Andrews
et al. 2008; Hamer and McDonnell 2008). Road density in an area as well as traffic
density on individual <strong>roads</strong> have been shown to have a negative effect on amphibian populations
(Eigenbrod et al. 2009; Fahrig and Rytwinski 2009; Hels and Buchwald 2001; Vos and
Chardon 1998). Veysey et al. (2011) even found road density to have a stronger effect on
population size than habitat availability, while Carr and Fahrig (2001) found more vagile species
to be more vulnerable to road mortality.
Very little literature exists on amphibians’ reactions to road. Amphibians are able to
recognise and avoid unsuitable habitat. Although <strong>the</strong>re are species specific variations, individuals
tend to prefer more shady and moist habitat types (Mazerolle 2005; Mazerolle and
Desrochers 2005; Popescu and Hunter 2011; Vos et al. 2007). In more open and dry habitats
like fields and clear-cuts, water loss is bigger and survival lower resulting in avoidance <strong>of</strong>
such habitats (Ro<strong>the</strong>rmel and Semlitsch 2002; Todd and Ro<strong>the</strong>rmel 2006). Individuals also
tend to move more quickly in inhospitable habitats (Hartung 1991; Tramontano 1997). These
observations suggest that amphibians should be able to avoid <strong>roads</strong>, however, <strong>the</strong> number <strong>of</strong>
road kills suggests <strong>the</strong> opposite (Elzanowski et al. 2009) and <strong>the</strong> only study on this topic did
not find any indication <strong>of</strong> road avoidance in Rana pipiens (Bouchard et al. 2009).
Pond breeding amphibians require both terrestrial and aquatic habitat to complete <strong>the</strong>ir
life cycle. Proximity between <strong>the</strong> required habitat types is important for <strong>the</strong> survival <strong>of</strong> <strong>the</strong>
population. Loss <strong>of</strong>, or diminished access to, one or both habitats will affect population size
and persistence probability (Dunning et al. 1992; Haynes et al. 2007; Johnson et al. 2007;
Pope et al. 2000). Moreover, populations <strong>of</strong> pond-breeding amphibians are frequently considered
to be structured as a regional network or a metapopulation, making dispersal between
63

Chapter Two
subpopulations essential to regional population persistence (Hels 2002; Marsh 2008; Marsh
and Trenham 2001; Smith and Green 2005). Thus <strong>the</strong> barrier effect caused by <strong>roads</strong> may have
severe consequences for populations <strong>of</strong> pond breeding amphibians.
We have developed an individual based model to assess <strong>the</strong> effects <strong>of</strong> infrastructure on
landscape connectivity. The model is part <strong>of</strong> a larger study concerning road effects on regional
populations <strong>of</strong> Moor frogs (Rana arvalis). In this paper we present our model and explore
how behavioural responses to infrastructure may affect local and regional connectivity.
The ability to avoid <strong>roads</strong> may diminish <strong>the</strong> amount <strong>of</strong> road kills. This behaviour will prevent
dispersal across <strong>the</strong> road but at <strong>the</strong> same time it may affect connectivity locally. Lower levels
<strong>of</strong> road avoidance can reduce <strong>the</strong> road’s barrier effect but this will probably depend on <strong>the</strong>
level <strong>of</strong> road mortality. We hypo<strong>the</strong>size that
Regional connectivity will be inhibited by high levels <strong>of</strong> road avoidance and high road
mortality and will depend on interactions between <strong>the</strong> degree <strong>of</strong> road avoidance and road
mortality
Local connectivity will be promoted by high levels <strong>of</strong> road avoidance but not be affected
by road mortality
We use a real Danish landscape with a population <strong>of</strong> Moor frogs traversed by a large road to
test how regional and local connectivity are affected by changes in road mortality and road
avoidance.
Methods
We use an individual based model to simulate <strong>the</strong> movements <strong>of</strong> juvenile Moor frogs and estimate
immigration probabilities between habitat patches. The purpose <strong>of</strong> <strong>the</strong> model is to
measure <strong>the</strong> connectivity <strong>of</strong> <strong>the</strong> landscape. In <strong>the</strong> following we use <strong>the</strong> terms dispersal and
migration as defined by Semlitsch (2008), i.e. dispersal is “interpopulational, unidirectional
movements from natal sites to o<strong>the</strong>r breeding sites” and migration is “intrapopulational,
round-trip movements toward and away from aquatic breeding sites”. The habitat <strong>of</strong> pond
breeding amphibians as <strong>the</strong> Moor frog includes terrestrial as well as aquatic habitat. Therefore
we define <strong>the</strong> habitat patch <strong>of</strong> a subpopulation as a complementary habitat patch containing
not only <strong>the</strong> breeding pond but also all accessible summer habitat within migration distance
from <strong>the</strong> pond (Dunning et al. 1992; Pontoppidan and Nachman In review; Pope et al. 2000).
64

Chapter Two
Model species
Moor frogs spend most <strong>of</strong> <strong>the</strong>ir life in terrestrial habitat; aquatic habitat is only used during
<strong>the</strong> breeding season, which takes place in <strong>the</strong> early spring (Elmberg 2008; Glandt 2008; Hartung
1991). Soon after breeding, <strong>the</strong> frogs return to <strong>the</strong> summer habitat, which lies mostly
within a 400 m radius from <strong>the</strong> breeding pond (Elmberg 2008; Hartung 1991; Kovar et al.
2009). Adult frogs show a high degree <strong>of</strong> site fidelity and <strong>of</strong>ten use <strong>the</strong> same breeding pond
and summer habitat from year to year (Loman 1994). Long distance dispersal in Moor frogs
takes place predominantly during <strong>the</strong> juvenile life-stage (Semlitsch 2008; Sinsch 1990; 2006).
Shortly after metamorphosis, <strong>the</strong> young frogs leave <strong>the</strong> natal pond and disperse into <strong>the</strong> surrounding
landscape seeking out suitable summer habitat. Dispersal distances are between a
few hundred meters up to 1-2 kilometres (Baker and Halliday 1999; Hartung 1991; Sinsch
2006; Vos and Chardon 1998). The juveniles stay in terrestrial habitat 2-3 years until <strong>the</strong>y
reach maturity, although some observations indicate that juvenile frogs follow <strong>the</strong> adults during
<strong>the</strong> spring migration, without entering <strong>the</strong> breeding ponds (Hartung 1991; Sjögren-Gulve
1998).
Model overview
The model considers a regional population <strong>of</strong> Moor frogs within a spatially explicit landscape
matrix. The landscape is constructed from a 600 x 800 cell GIS raster map, each cell representing
an area <strong>of</strong> 10 x 10 meters. A raster cell is characterised by a set <strong>of</strong> variables defining
<strong>the</strong> habitat type and its value in regard to <strong>the</strong> different aspects <strong>of</strong> <strong>the</strong> life cycle and behaviour
<strong>of</strong> <strong>the</strong> Moor frog (Table 1). Potential sites for subpopulations <strong>of</strong> Moor frogs are represented
by a GIS point-data set <strong>of</strong> ponds surveyed during field work. Each pond is defined by an IDnumber,
a quality index and <strong>the</strong> summer habitat fragments located within migration distance
from <strong>the</strong> pond (Table 1).
Immigration requires two events: 1) <strong>the</strong> successful dispersal <strong>of</strong> a juvenile frog to summer
habitat outside its natal habitat patch and 2) subsequent successful migration from <strong>the</strong>
new summer habitat to a nearby breeding pond. In real life dispersal starts just after metamorphosis
in early summer and lasts until hibernation in <strong>the</strong> autumn. The second part <strong>of</strong> <strong>the</strong> immigration
event, migration, takes place in <strong>the</strong> spring 2.5 years later. For simplicity, we simulate
<strong>the</strong> dispersal and breeding migration, as if <strong>the</strong>y take place in <strong>the</strong> same year.
65

Chapter Two
The time step <strong>of</strong> <strong>the</strong> model is one day and <strong>the</strong> simulated period for dispersal as well as
migration is 120 days each. At <strong>the</strong> start <strong>of</strong> a simulation, 500 frog agents are created at each
pond. Each agent is assigned a random direction, which determines its preferred direction <strong>of</strong>
movement. This direction does not change unless summer habitat is found. At each time step,
a random daily travelling distance is chosen for each agent; <strong>the</strong> distance depending on <strong>the</strong>
attractiveness <strong>of</strong> <strong>the</strong> current habitat. The distance is travelled one cell at a time, moving to one
<strong>of</strong> <strong>the</strong> neighbouring cells, depending on <strong>the</strong> relative attractiveness <strong>of</strong> <strong>the</strong> cells, although backwards
movement is not allowed. The movement rules generate a biased random walk away
from <strong>the</strong> natal pond and in <strong>the</strong> preferred direction. During dispersal, frog agents encountering
a cell with summer habitat will have a certain probability <strong>of</strong> settling in <strong>the</strong> habitat and stop
dispersing. This probability will increase with time. At <strong>the</strong> end <strong>of</strong> <strong>the</strong> dispersal period all frog
agents that have not settled in summer habitat are removed. Starting <strong>the</strong> migration phase, <strong>the</strong>
remaining frog agents move toward <strong>the</strong> breeding pond associated with <strong>the</strong>ir summer habitat;
in case several breeding ponds are available one is chosen randomly weighted by pond quality.
After each time step, <strong>the</strong> survival probability <strong>of</strong> every frog agent is assessed, based on <strong>the</strong>
daily survival rates associated with <strong>the</strong> habitat type traversed during <strong>the</strong> day. Full model
documentation is found in Appendix 1 in <strong>the</strong> supplementary material, following <strong>the</strong> ODDtemplate
suggested by Grimm et al. (2006; 2010). Netlogo v.4.1.3 (Wilensky 1999) is used as
modelling environment (freely downloadable at http://ccl.northwestern.edu/netlogo).
Input data
We use GIS data sets from a road project in Denmark, supplied by <strong>the</strong> Danish Road Directorate
and Amphi Consult. The project concerns an area in north-western part <strong>of</strong> Zealand, 10 km
east <strong>of</strong> <strong>the</strong> city <strong>of</strong> Kalundborg (55° 40.14’ N 11° 17.85’ E) (Fig. 1). The area is characterised
as semi-urban and agricultural landscapes, traversed by creeks and wetlands. A project data
set contains a land cover map <strong>of</strong> <strong>the</strong> area and a point-data set <strong>of</strong> potential breeding ponds
found during field surveys. The land cover maps are constructed following a protocol designed
by amphibian experts (Hassingboe et al. 2012), in which a range <strong>of</strong> different habitat
types are identified. Each habitat type has been assessed and ranked on a scale from 1- 5, for
<strong>the</strong> following three variables: <strong>the</strong> habitat’s relative suitability as summer habitat (H q ), its relative
attraction to frogs during movement (H a ) and <strong>the</strong> relative survival probability (H s ) in <strong>the</strong>
habitat. In <strong>the</strong> model <strong>the</strong> survival index (H s ) is converted into a daily survival probability (D s )
(see appendix 1 for details). Infrastructural elements like <strong>roads</strong> and railways are processed as
66

Chapter Two
any o<strong>the</strong>r habitat type and assigned values <strong>of</strong> habitat attraction and daily survival. However,
in <strong>the</strong> literature <strong>the</strong> terms “road avoidance” and “road mortality” are more commonly used. To
avoid confusion when discussing <strong>the</strong>se effects, we <strong>the</strong>refore convert (H a ) and (D s ) to road
avoidance (R a ) and road mortality (R d ), respectively, and invert <strong>the</strong> ranking, i.e. R a = 6 - H a
and R d = 1 - D s .
The point-data set contains information on <strong>the</strong> location <strong>of</strong> <strong>the</strong> potential breeding pond,
its ID-number as well as a quality index (Q). Pond qualities ranges from 0.1 – 1 and relates to
<strong>the</strong> suitability <strong>of</strong> <strong>the</strong> pond and <strong>the</strong> immediate surroundings in regard to egg and larval survival
and are estimated by experts during field work. In this paper we have excluded low-quality
ponds (Q < 0.6), since <strong>the</strong>y per definition have a low probability <strong>of</strong> maintaining a population
on <strong>the</strong>ir own. The extent <strong>of</strong> <strong>the</strong> map is 6x8 km and it contains 40 ponds.
Scenarios
We create scenarios with increasing values <strong>of</strong> road avoidance, R a = [1; 2; 3; 4; 5], and road
mortality, R d = [0.1; 0.3; 0.5; 0.7; 0.9], <strong>of</strong> <strong>the</strong> two major <strong>roads</strong> cutting through <strong>the</strong> map (Fig.1,
<strong>roads</strong> shown in red). We run 25 simulations for every combination <strong>of</strong> <strong>the</strong> parameter values <strong>of</strong>
R a and R d . As R a increases <strong>the</strong> willingness <strong>of</strong> <strong>the</strong> frog agents to enter <strong>the</strong> road will decrease,
while <strong>the</strong> probability <strong>of</strong> surviving will increases with decreasing values <strong>of</strong> R d .
Output
At <strong>the</strong> end <strong>of</strong> each simulation, <strong>the</strong> natal pond and <strong>the</strong> breeding pond <strong>of</strong> all frog agents are registered
and immigration probability (p ij ) between all pair-wise ponds is calculated. Landscape
connectivity (S) is <strong>the</strong>n found as
∑ ∑
,
(eq.1)
Local populations are identified by grouping ponds into clusters depending on <strong>the</strong>ir mutual
connectivity, using <strong>the</strong> method <strong>of</strong> unweighted, arithmetic, average clustering as described by
Legendre and Legendre (1998). Since, immigration probabilities between any two ponds are
not necessarily symmetric, i.e. p ij ≠ p ji , we use summed immigrations probabilities as similarity
measure (m): m ij = p ij + p ji . The threshold at which a given pond or cluster no longer can
be added to ano<strong>the</strong>r cluster is set to m ij ≤ 0.01. We define local connectivity as <strong>the</strong> connectivity
within a cluster and regional connectivity is defined as <strong>the</strong> connectivity between all
67

Chapter Two
pair-wise combinations <strong>of</strong> clusters. Based on <strong>the</strong> clustering result we compute within-cluster
connectivity (S c ) for each cluster as
∑ ∑
,
(eq. 2)
where n c is <strong>the</strong> number <strong>of</strong> ponds belonging to cluster c. Connectivity between clusters (S b ) is
<strong>the</strong>n found as S b = S – S c . However, to be able to detect changes in local connectivity, <strong>the</strong>
ponds constituting a cluster must be <strong>the</strong> same in all scenarios. Therefore, we use <strong>the</strong> cluster
configuration found when R a is set to 5 to define clusters, and use this in all calculations <strong>of</strong>
within-cluster connectivity.
We use a multiple regression model, with <strong>the</strong> general form y = β 0 + β 1 R d + β 2 R a +
β 3 R d R a + ε., to test for <strong>the</strong> effect <strong>of</strong> road avoidance (R a ), road mortality (R d ) and <strong>the</strong>ir interaction
on landscape connectivity (S), within-cluster connectivity (S c ) and between-cluster connectivity
(S b ). Sequential Holm-Bonferroni correction is used to adjust p-values. When R a is
set to 5, frog agents to do not enter <strong>the</strong> road, <strong>the</strong>refore <strong>the</strong> level <strong>of</strong> road mortality is inconsequential.
Moreover, preliminary tests showed extreme connectivity values when <strong>the</strong> road is
100% blocked. Both <strong>of</strong> <strong>the</strong>se factors risk masking <strong>the</strong> statistical effect <strong>of</strong> road mortality and
road avoidance on connectivity at o<strong>the</strong>r levels <strong>of</strong> R a . Consequently, <strong>the</strong> results from <strong>the</strong> scenarios
with R a = 5 are excluded from <strong>the</strong> statistical testing.
Results
Analyses <strong>of</strong> <strong>the</strong> scenarios with R a = 5 identifies seven clusters (Fig. 2A Table 2). Cluster c1
contains four ponds and is located ra<strong>the</strong>r remotely in <strong>the</strong> top <strong>of</strong> <strong>the</strong> map. Clusters c2 and c3
are found in areas close to where <strong>the</strong> two test <strong>roads</strong> cross and contains four, respectively, five
ponds. Cluster c4 and cluster c5 contains seven and nine ponds, respectively. These are more
widespread clusters situated on ei<strong>the</strong>r side <strong>of</strong> <strong>the</strong> road in <strong>the</strong> middle <strong>of</strong> <strong>the</strong> map. The last two
clusters c6 and c7 are placed near <strong>the</strong> bottom <strong>of</strong> <strong>the</strong> map and contain two and six ponds. As
described in <strong>the</strong> method section we use this cluster configuration as a reference for all scenarios
when calculating within-cluster connectivity. None<strong>the</strong>less, <strong>the</strong> analyses show that cluster
configurations do not change with <strong>the</strong> different scenarios except when road mortality is set to
0.1. In this case dispersal success is sufficiently high between cluster c4 and c5 and <strong>the</strong>y fuse
into one cluster (Fig. 2B).
68

Chapter Two
When R a ≤ 4, road mortality has strong negative effect on <strong>the</strong> connectivity between
clusters (S b ) while road avoidance has a positive effect. Fur<strong>the</strong>rmore, <strong>the</strong>re is an interaction
effect; <strong>the</strong> effect <strong>of</strong> road avoidance becomes more pronounced as road mortality decreases
(Table 3). These effects are all statistically significant (F 3,496 = 1814, p

Chapter Two
quickly leave it again and only suffer <strong>the</strong> high mortality for at short time. When road avoidance
is low, frog agents enter <strong>the</strong> <strong>roads</strong> more willingly and will tend to stay <strong>the</strong>re, suffering
from <strong>the</strong> higher mortality for a longer time. The severity <strong>of</strong> <strong>the</strong> “trap” effect will depend on
road mortality as, all else being equal, successful dispersal across <strong>the</strong> road depends on <strong>the</strong>
survival probability. The results do in fact show a strong interaction; <strong>the</strong> positive effect <strong>of</strong>
road avoidance on between-cluster connectivity getting more pronounced as road mortality
increases.
In accordance with our second hypo<strong>the</strong>sis, we find that road avoidance has a positive effect
on local connectivity. In particular, when road avoidance is set to five, connectivity
shows considerable elevated values. The strong effect on within-cluster connectivity <strong>of</strong> a 100
% barrier may seem surprising, but can be explained as a “deflection” effect. When <strong>the</strong> road is
inaccessible road mortality is no longer an issue and a larger proportion <strong>of</strong> frog agents will
survive. Moreover, <strong>the</strong> blockage forces <strong>the</strong> agents to move along <strong>the</strong> road instead <strong>of</strong> crossing.
Taken toge<strong>the</strong>r, this has <strong>the</strong> effect that a larger proportion <strong>of</strong> frog agents stay within <strong>the</strong> local
area for a longer time, which increases <strong>the</strong> probability <strong>of</strong> an agent settling within <strong>the</strong> cluster,
enhancing within-cluster connectivity. We did not expect road mortality to have an effect on
within-cluster connectivity, but we do find a negative, although week, response. This is
probably because <strong>the</strong>re will be a small proportion <strong>of</strong> frog agents entering <strong>the</strong> road and returning
to <strong>the</strong> same side. The survival probability <strong>of</strong> <strong>the</strong>se returnees will depend on road mortality.
The seven clusters identified in this study do not all respond in <strong>the</strong> same way on
changes in road avoidance and road mortality. Two <strong>of</strong> <strong>the</strong> clusters, c1 and c7, are not affected
at all; <strong>the</strong>se are also <strong>the</strong> clusters fur<strong>the</strong>st away from <strong>the</strong> road. Road mortality only significantly
affects larger clusters with several pond members very close to <strong>the</strong> road; maybe because
only <strong>the</strong>se clusters have sufficient number <strong>of</strong> returnees for <strong>the</strong> effect to be detectable.
Road avoidance, on <strong>the</strong> o<strong>the</strong>r hand, affects also clusters fur<strong>the</strong>r away; only clusters with a
minimum distance to road above 300 m are unaffected by road avoidance. The result suggests
that if <strong>the</strong> road is within <strong>the</strong> summer habitat <strong>of</strong> some <strong>of</strong> <strong>the</strong> member ponds, <strong>the</strong>n road avoidance
will affect within-cluster connectivity.
In this study, scenarios with road avoidance set to five, corresponds to real life situations
where fencing along <strong>roads</strong> prevents access to <strong>the</strong> road. Our results suggest that fencing
70

Chapter Two
can result in highly increased local connectivity, even between ponds not in immediate proximity
to <strong>the</strong> road. Thus, fencing may not just mitigate road induced mortality but may actually
enhance local population persistence. Depending on number, quality and connectivity between
subpopulation on <strong>the</strong> same side <strong>of</strong> <strong>the</strong> road a streng<strong>the</strong>ning <strong>of</strong> subpopulations adjacent
to road fences can potentially improve regional population persistence (Hels and Nachman
2002). However, fencing also separates a population into several smaller and more isolated
groups <strong>of</strong> subpopulations, each <strong>of</strong> which may have a higher risk <strong>of</strong> extinction and a lower
probability <strong>of</strong> recolonisation. In a simulation experiment with a local population <strong>of</strong> virtual
animals Jaeger and Fahrig (2004) found that fencing could prolong persistence time but had
little effect on persistence probability, and in most cases <strong>the</strong> population only survived on one
side <strong>of</strong> <strong>the</strong> road.
The series <strong>of</strong> scenarios are hypo<strong>the</strong>tical and all may not correspond to real life situations
but road mortality can indeed range between very low and very high values, depending on
traffic intensity. Extreme low values <strong>of</strong> road avoidance, to <strong>the</strong> point where <strong>the</strong> road becomes
more attractive than <strong>the</strong> surrounding landscape, may seem very unrealistic. However, behavioural
responses to traffic like immobilisation (Mazerolle et al. 2005) can have similar effects;
and after rain fall wet, dark <strong>roads</strong> may appear deceptively attractive to frogs (Andrews et al.
2008).
Our study concerns a specific landscape and a specific species, but still it is possible to
draw some general conclusion. First <strong>of</strong> all our results emphasize that connectivity is context
dependent. The behaviour <strong>of</strong> <strong>the</strong> focal species, <strong>the</strong> structure <strong>of</strong> <strong>the</strong> landscape and <strong>the</strong>ir interaction
are essential to how connectivity is realized. Fur<strong>the</strong>rmore, our simulations indicate that
<strong>roads</strong> not only affect dispersal across <strong>roads</strong>. Even between ponds located on <strong>the</strong> same side <strong>of</strong>
<strong>the</strong> road, dispersal success can be highly susceptible to road avoidance and road mortality,
depending on <strong>the</strong> distance to <strong>the</strong> road. This suggests that <strong>roads</strong> may affect not only regional or
metapopulation dynamics but also have a direct effect on local population dynamics.
Acknowledgements
The work was funded by <strong>the</strong> Danish Road Directorate. The Amphi Consult group has provided
amphibian expertise as well as map data. Marianne Ujvári, Martin Hesselsøe, Agnete
Jørgensen and Martin Schneekloth have given valuable feed-back during <strong>the</strong> model develop-
71

Chapter Two
ment. Uta Berger has given precious help during <strong>the</strong> work and kept <strong>the</strong> main author on <strong>the</strong>
IBM-track. We are very thankful to Carolyn Bauer for linguistic help.
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Chapter Two
Wilensky U (1999) NetLogo. Center for Connected Learning and Computer-Based Modeling,
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Figure legends
Figure 1
Study area. A) Location <strong>of</strong> two study areas in Denmark. KaB is an area near Kalundborg on
Zealand and HoB is near Holstebro in Jutland. Only KaB is used in <strong>the</strong> present analysis, but
both areas are used for <strong>the</strong> parameterisation <strong>of</strong> <strong>the</strong> model. B) KaB map used in <strong>the</strong> analysis.
Black dots are breeding ponds, test <strong>roads</strong> are marked with red.
Figure 2
Results from cluster analyses with two different parameter settings. A) R a = 5, R d = 0.1 and B)
R a = 4, R d = 0.9
Figure 3
Effect <strong>of</strong> road avoidance (R a ) and road mortality (R d ) on a) between-cluster connectivity (S b )
and b) landscape connectivity (S)
Figure 4
Effect <strong>of</strong> road avoidance (R a ) and road mortality (R d ) on within-cluster connectivity (S c ) in
cluster c2 – c6
75

Chapter Two
Figures
Figure 1
76

Chapter Two
Figure 2
Figure 3
77

Chapter Two
Figure 4
78

Chapter Two
Tables
Table 1 List <strong>of</strong> variables characterizing <strong>the</strong> agents in <strong>the</strong> model
Variable
Notation
Value
range
Agent
type
Description
DailySurvival D s Cell Daily survival probability
HabitatAttraction H a 1-5 Cell
The cell’s relative attraction to frogs during
movement
HabitatCode H c Cell Cell code for habitat type
HabitatSurvival H s 1-5 Cell The cell’s relative survival index
SummerQuality H q 1-5 Cell
The cell’s relative suitability as summer
habitat
BreedingPond Frog Breeding pond <strong>of</strong> frog agent
NatalPond Frog Natal pond <strong>of</strong> frog agent
PondID Pond ID number
PondQuality Q 0.1-1 Pond Quality index <strong>of</strong> <strong>the</strong> pond
SummerHabitat A Pond
Summer habitat cells associated with <strong>the</strong>
pond
79

Chapter Two
Table 2 Descriptive statistics <strong>of</strong> <strong>the</strong> identified clusters.
The cluster’s ID, number <strong>of</strong> ponds in <strong>the</strong> cluster, mean distance from <strong>the</strong> ponds to a road, <strong>the</strong>
distance to <strong>the</strong> pond closest to <strong>the</strong>n road and <strong>the</strong> number <strong>of</strong> pond members no more than 200
m from <strong>the</strong> road. Fur<strong>the</strong>rmore it is shown whe<strong>the</strong>r <strong>the</strong> cluster exhibits extreme connectivity
values when R a =5, its response to road avoidance and its response to road mortality
Cluster characteristics
Responds patterns
Cluster
Cluster
Mean dis-
Min distance
Ponds
R a =
Avoid-
Mortal-
Id
size
tance (m)
( m)
200m
5
ance
ity
c1 4 1322 1082 0 N N N
c2 4 184 110 3 Y Y N
c3 5 345 76 1 Y Y N
c4 7 431 61 2 Y Y Y
c5 9 223 71 6 Y Y Y
c6 6 323 98 1 Y N N
c7 2 385 318 0 N N N
80

Chapter Two
Table 3 Statistical results <strong>of</strong> multiple regression models
Statistical significance <strong>of</strong> variables and interactions in multiple regressions on landscape connectivity
(S), within-cluster connectivity (S c ) <strong>of</strong> cluster c1 – c7 and between-cluster connectivity
(S b ). Sequential Holm-Bonferroni correction is used to adjust p-values. Statistically significant
values are shown in bold.
Full model Road mortality R d Road avoidance, R a Interaction R a * R d
p
p
Dependent
Parameter
df F p R 2
factor
Parameter
Parameter
p
Sc1 496 0.30 0.82 0.002 -0.003 0.873 0.001 0.738 0.001 0.884
Sc2 496 7.20

Chapter Two
Supplementary material - Appendix 1
Model ODD
Purpose
The purpose <strong>of</strong> <strong>the</strong> model is to measure <strong>the</strong> connectivity <strong>of</strong> <strong>the</strong> landscape. In this study connectivity
between any two subpopulations is measured as <strong>the</strong> probability <strong>of</strong> successful immigration.
The habitat <strong>of</strong> pond breeding amphibians as <strong>the</strong> Moor frog includes terrestrial as well
as aquatic habitat. Therefore, <strong>the</strong> habitat patch <strong>of</strong> a subpopulation is modelled as a complementary
habitat patch containing not only <strong>the</strong> breeding pond but also all accessible summer
habitat within migration distance from <strong>the</strong> pond (Dunning et al. 1992; Pontoppidan and
Nachman In review; Pope et al. 2000). Immigration, thus, requires two events: 1) <strong>the</strong> successful
dispersal <strong>of</strong> a juvenile frog to summer habitat outside its natal habitat patch and 2) subsequent
successful migration to a breeding pond associated with <strong>the</strong> new summer habitat. In real
life <strong>the</strong>se two events is 2 year apart, but, for simplicity, we only simulate <strong>the</strong> dispersal and
migration events not <strong>the</strong> intervening years.
Entities, state variables, and scales
Breeding ponds are treated as stationary agents. Each pond agent is characterized by a unique
id-number, pond-quality and <strong>the</strong> associated summer habitat. Frog agents are characterized by
<strong>the</strong> pond in which <strong>the</strong>y are hatched and <strong>the</strong> breeding pond <strong>the</strong>y immigrate to. The extent <strong>of</strong>
<strong>the</strong> model landscape is 600 x 800 grid cells, and each grid cell represents 10 x 10 m. Grid
cells are defined by <strong>the</strong>ir relative attraction to dispersing frogs, a habitat survival index and a
daily survival probability, <strong>the</strong> habitat type and <strong>the</strong> relative value as summer habitat (see Table
1 in main text). The first part <strong>of</strong> <strong>the</strong> simulation mimics <strong>the</strong> dispersal <strong>of</strong> newly metamorphosed
frogs, starting in mid-summer until hibernation in autumn. The second part considers <strong>the</strong>
spring movement <strong>of</strong> juveniles from <strong>the</strong> summer habitat towards <strong>the</strong>ir future breeding pond
and back to <strong>the</strong>ir summer habitat. Each part runs for 120 time steps, one step representing one
day.
Process overview and scheduling
At <strong>the</strong> start <strong>of</strong> a simulation, 500 frog agents are located at each pond agent and <strong>the</strong> frog variable
NatalPond is updated with <strong>the</strong> ID-number <strong>of</strong> <strong>the</strong> pond. In <strong>the</strong> first part <strong>of</strong> <strong>the</strong> simulation
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Chapter Two
(dispersal) <strong>the</strong> following procedures are executed each time-step: Move (movement <strong>of</strong> frog
agents), Settle (evaluates if a frog agent stops dispersing and assigns frogs to breeding ponds)
and Survival (evaluates if a frog agent survives). At day 120 <strong>the</strong> dispersal stops; frog agents
that have not settled are removed and <strong>the</strong> migration simulation starts. The two procedures
Move and Survival are run every time step and settled frogs start moving again, this time
towards <strong>the</strong>ir breeding pond. When a frog reaches its assigned breeding pond, its direction is
set towards one <strong>of</strong> <strong>the</strong> summer habitat fragments associated with <strong>the</strong> breeding pond. The
simulation stops at day 240 and at each pond <strong>the</strong> model counts <strong>the</strong> number <strong>of</strong> immigrants
from each <strong>of</strong> <strong>the</strong> o<strong>the</strong>r pond agents, computing immigration probabilities between all pairs <strong>of</strong>
ponds. The simulation is repeated 25 times.
Design concepts
Emergence
Immigration rates will emerge as a response to <strong>the</strong> landscape configuration.
Adaptation & Objectives
To avoid desiccation and <strong>the</strong>reby increase survival, frog agents are assumed to move in response
to <strong>the</strong> moistness <strong>of</strong> its surroundings. In general, <strong>the</strong> moister a habitat is <strong>the</strong> more attractive
<strong>the</strong> habitat is for <strong>the</strong> frog as indicated by <strong>the</strong> habitat-attraction parameter H a . Dispersing
juvenile Moor frogs have an innate tendency to move away from <strong>the</strong>ir natal pond. Each
frog agent is assigned a random direction to move, but during dispersal <strong>the</strong> frog adjusts its
path to <strong>the</strong> encountered habitat. Adjustments are centred about <strong>the</strong> preferred direction in a
way that prevents backtracking.
Sensing
Frog agents are assumed to be aware <strong>of</strong> <strong>the</strong>ir own state-variables. Frog agents are also aware
<strong>of</strong> <strong>the</strong> habitat attraction <strong>of</strong> <strong>the</strong> grid cells, as well as <strong>the</strong> identity <strong>of</strong> <strong>the</strong> pond agents.
Interaction
There is no interaction between frog agents. Movement decisions <strong>of</strong> <strong>the</strong> frog agents depend on
<strong>the</strong> habitat attraction <strong>of</strong> <strong>the</strong> neighbouring cells. Survival <strong>of</strong> <strong>the</strong> frog agents depends on <strong>the</strong>
daily survival rates <strong>of</strong> <strong>the</strong> traversed habitat.
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Chapter Two
Stochasticity
Which cell to move to, is chosen randomly among <strong>the</strong> neighbouring cells with <strong>the</strong> probability
<strong>of</strong> being chosen weighted by <strong>the</strong> habitat-attraction <strong>of</strong> <strong>the</strong> neighbouring cells. If frog agents
occupy a cell suitable as summer habitat <strong>the</strong>y will stop dispersing with a certain probability;
<strong>the</strong> probability increases with time. The breeding pond <strong>of</strong> a settled frog agent is chosen randomly
among accessible pond agents weighted by pond-quality.
Observation
At <strong>the</strong> end <strong>of</strong> each simulation, <strong>the</strong> natal pond and breeding pond <strong>of</strong> all frog agents are registered
and immigration probability (p ij ) between all pair-wise pond agents is calculated.
Initialization
A landscape is constructed based on a GIS-raster data set. Each cell contains information
about habitat type, habitat attraction, habitat survival and summer quality. A data set with
information on location, ID-number and pond quality <strong>of</strong> surveyed ponds is used to create
pond agents. Once <strong>the</strong> landscape is created, <strong>the</strong> Map-scan procedure is run to identify all accessible
summer habitat cells associated with each pond agents and <strong>the</strong> pond variable A is
updated. Habitat survival is converted into daily survival probabilities and <strong>the</strong> cell variable D s
is updated. 500 frog agents are located on each pond agent, <strong>the</strong>ir direction set randomly.
Submodels
Map-scan
The cell variable DailySurvival (D s ) is set as <strong>the</strong> probability <strong>of</strong> a frog agent surviving one time
step in <strong>the</strong> cell. This depends on <strong>the</strong> habitat code (H c ) and <strong>the</strong> habitat survival index (H s ) <strong>of</strong>
<strong>the</strong> cell. Cells belonging to <strong>roads</strong>, H c = [2, 3, 4 5], are assign D s values specific for <strong>the</strong>ir habitat
code (see Appendix 1, Parameterisation). All o<strong>the</strong>r cells are modelled as
1∨ 6 , where σ0 and σ 1 are species specific constants.
Local populations <strong>of</strong> pond-breeding amphibians inhabit a kind <strong>of</strong> composite habitat patch. At
its core <strong>the</strong> breeding pond is located, surrounded by satellites <strong>of</strong> summer habitat fragments
separated by matrix habitat (Pontoppidan and Nachman In review). The Map-scan procedure
delimits <strong>the</strong> extent <strong>of</strong> <strong>the</strong> habitat patch as all accessible cells within a 40 cells (400 m) radius
from <strong>the</strong> pond. Accessible cells are defined as cells with habitat attraction (H a ) greater than 1
84

Chapter Two
and daily survival (D s ) greater than 0.3. This excludes structures such as buildings and large
<strong>roads</strong>. Fur<strong>the</strong>rmore, inaccessible cells functions as a barrier blocking access to <strong>the</strong> habitat behind
(Eigenbrod et al. 2008) (Fig.A1).
Move
Each day frog agents move a randomly chosen distance depending on <strong>the</strong> habitat attraction
(H a ) <strong>of</strong> its current cell. The distance is drawn from a normal distribution with a mean <strong>of</strong> c and
standard deviation <strong>of</strong> s. Assuming <strong>the</strong> frog to head in <strong>the</strong> direction it was assigned when it left
<strong>the</strong> natal pond, it moves to one <strong>of</strong> its neighbouring cells located within ±90 0 from <strong>the</strong> preferred
direction. Cells with H a = 1 is considered inaccessible. Based on habitat attraction <strong>of</strong>
<strong>the</strong> neighbouring, accessible cells (n), frog agents first decide which kind <strong>of</strong> habitat <strong>the</strong>y want
to move to. The probability <strong>of</strong> moving into one <strong>of</strong> <strong>the</strong> cells with habitat attraction H a is found
as
∑
1 , where n a is <strong>the</strong> number <strong>of</strong> neighbouring cells with habitat attraction
H a and H ai is <strong>the</strong> habitat attraction <strong>of</strong> cell i. A uniform pseudorandom number is selected
to choose <strong>the</strong> type <strong>of</strong> habitat. If <strong>the</strong>re is more than one neighbouring cell with <strong>the</strong> chosen habitat
attraction, one <strong>of</strong> <strong>the</strong>m is chosen randomly. The frog agent <strong>the</strong>n moves to a random position
within <strong>the</strong> cell, without changing its direction. This routine is repeated until <strong>the</strong> chosen
distance for <strong>the</strong> day is traversed.
During <strong>the</strong> second part <strong>of</strong> <strong>the</strong> simulation, as frog agents get within a distance <strong>of</strong> two
cells from <strong>the</strong>ir destination (breeding pond agent or summer habitat cell), <strong>the</strong> frogs move directly
to it. At <strong>the</strong> breeding pond frog agents are randomly assigned a summer habitat cell
associated with <strong>the</strong> habitat patch. When <strong>the</strong> frogs reach <strong>the</strong>ir summer habitat cell <strong>the</strong>y stop
moving. Frog agents reaching <strong>the</strong> boundary <strong>of</strong> <strong>the</strong> landscape are removed. If frogs agents are
cornered with no accessible habitat to move to, <strong>the</strong>ir direction is permanently changed ei<strong>the</strong>r
35 degrees to <strong>the</strong> left or to <strong>the</strong> right.
Settle
Dispersing frog agents encountering a summer habitat cell has a certain probability <strong>of</strong> settling.
The probability depends on <strong>the</strong> day number <strong>of</strong> <strong>the</strong> year (t) and is found as:
, where ν 0 and ν 1 are species specific constants
85

Chapter Two
When <strong>the</strong> summer habitat cell in which <strong>the</strong> frog agent has settled is part <strong>of</strong> a habitat patch, <strong>the</strong>
frog is assigned <strong>the</strong> associated pond agent. If <strong>the</strong> summer habitat cell is shared by several
pond agents, <strong>the</strong> probability <strong>of</strong> being assigned a pond agent i is a function <strong>of</strong> <strong>the</strong> pond quality
(Q) <strong>of</strong> <strong>the</strong> available pond agents (n):
until <strong>the</strong> second part <strong>of</strong> <strong>the</strong> simulation.
Survival
∑
. Once a frog agent is settled it stops moving
For each frog agent a pseudo-random number is drawn between 0 and 1. If <strong>the</strong> number exceeds
<strong>the</strong> geometric average <strong>of</strong> daily survival (D s ) <strong>of</strong> <strong>the</strong> cells traversed during <strong>the</strong> day, <strong>the</strong>
agent dies.
Parameterisation
All parameter values are listed in Table A1.
Habitat attraction (H a )
Terrestrial amphibians are assumed to prefer habitat in which <strong>the</strong> water content is high
<strong>the</strong>reby minimizing <strong>the</strong> risk <strong>of</strong> desiccation. In an experiment with nor<strong>the</strong>rn green and nor<strong>the</strong>rn
leopard frogs in peatlands Mazerolle and Desrochers (2005) found that 18 out <strong>of</strong> 25 frogs
(72%) avoided barren surface. Hartung (1991) found that Moor frogs avoided areas with
sparse or low vegetation, and recorded <strong>the</strong> ratio between densities in grass areas and densities
in moor lands, hedges, ditches and forests to be 1:3.5.
In <strong>the</strong> model, <strong>the</strong> probability <strong>of</strong> a frog agent choosing one type <strong>of</strong> cell above ano<strong>the</strong>r
during movement <strong>the</strong>refore depends on <strong>the</strong> attractiveness <strong>of</strong> <strong>the</strong> cells habitat type. The habitat
attraction (H a ) <strong>of</strong> <strong>the</strong> different habitat types in <strong>the</strong> GIS maps was guesstimated by amphibian
specialists (Table A2). We tested three different expressions <strong>of</strong> H a to enter into <strong>the</strong> Moveprocedure:
a) H a , b) (H a ) 2 and c) exp(H a ) and compared <strong>the</strong> results with <strong>the</strong> above mentioned
empirical findings. In addition, we also ran a simulation where movement was independent on
habitat attraction.
As test landscapes we used GIS data sets from two different road projects in Denmark,
supplied by <strong>the</strong> Danish Road Directorate and Amphi Consult. The first project (KaB) concerns
an area in north-western part <strong>of</strong> Zealand, 10 km east <strong>of</strong> <strong>the</strong> city <strong>of</strong> Kalundborg (55°
40.14’ N 11° 17.85’ E); <strong>the</strong> second project (HoB) is from central Jutland, ca. 5 km east <strong>of</strong>
86

Chapter Two
Holstebro (56° 19.66’ N 8° 44.65’ E) (Fig. 1). Both areas are characterised as semi-urban and
agricultural landscapes, traversed by creeks and wetlands. In <strong>the</strong> HoB map 36% <strong>of</strong> all cells
were classified as attractive habitat (H a > 3) and <strong>the</strong> KaB map contained 51% attractive habitat.
The model was run for 40 time steps without <strong>the</strong> Settle-procedure, and <strong>the</strong> ratio between
frog agents in attractive (H a = 4 or 5) and unattractive (H a = 2 or 3) habitat was computed as
well as <strong>the</strong> percentage <strong>of</strong> frog agents in attractive habitat. Although <strong>the</strong>re were differences
between <strong>the</strong> maps, we chose <strong>the</strong> expression exp(H a ) as being <strong>the</strong> best to reproduce <strong>the</strong> empirical
patterns (Table A3).
Distance travelled pr. day
In a radio tracking experiment with common frog (Rana temporaria) Tramontano (1997)
found adult frogs moving through a rye field to cover 148 m in one week, corresponding to ca
20 m pr day. In a study on dispersing juvenile moor frogs Hartung (1991) reported daily travelling
distances <strong>of</strong> 12.5–18.8 m (mean 15.5 m) in attractive habitat as moors and 39.9–40.9 m
in unattractive areas as pine forests. The daily travelling distance is, thus, assumed to depend
on habitat attraction <strong>of</strong> <strong>the</strong> current cell and is modelled as following a normal distribution
with a mean <strong>of</strong> c/H a and standard deviation s.
Two homogenous landscapes were constructed with a habitat attraction <strong>of</strong> 2 or 4, respectively.
In each landscape frog agents were allowed to move according to <strong>the</strong> Moveprocedure
for 40 time steps. When a simulation ended <strong>the</strong> straight distance between start and
end point for all frog agents was measured and <strong>the</strong> mean daily travelling distance computed.
The simulations were conducted for varying values <strong>of</strong> c and s, each combination repeated 50
times. A parameter set was sought where daily travelling distance
in attractive habitat exhibited values in <strong>the</strong> range between 12 m and 19 m and with a mean
around 15 m
in unattractive habitat exhibited values in a range between 20 m and 40 m
The parameter set (c=7, s=0.5) was chosen as <strong>the</strong> best to fulfil <strong>the</strong> conditions.
Settle
Little data has been found on dispersal distances. Hartung (1991) found dispersal distances <strong>of</strong>
newly metamorphosed moor frogs up to 1200 m, but mean dispersal distance is guesstimated
by experts to be 200-300 m. As <strong>the</strong> new frogs are assumed to have an innate urge to move
87

Chapter Two
away from <strong>the</strong>ir natal pond, settling probability is expected to be low in <strong>the</strong> beginning. The
dispersal drive is expected to subside with time, with settling probability increasing accordingly,
creating an s-shaped probability function (Fig.A2). The realized dispersal distances will
depend on <strong>the</strong> landscape configuration. With <strong>the</strong> chosen parameter set (ν 0 , ν 1 ) mean dispersal
distance <strong>of</strong> frog agents in <strong>the</strong> HoB map is 363 m and max. dispersal distance is 2068 m. 68%
<strong>of</strong> <strong>the</strong> frog agents settle within <strong>the</strong>ir own habitat patch. Less than 2% <strong>of</strong> <strong>the</strong> frog agents disperse
more than 1000 m. In <strong>the</strong> KaB map mean and maximum dispersal distances are 291 m
and 2151 m, respectively. 83% settle within <strong>the</strong> home patch and less than 0.5% disperse more
than 1000 m (Fig.A3).
Daily survival
The survival probability <strong>of</strong> dispersing frogs is assumed to depend on <strong>the</strong> habitat. No empirical
data on daily survival probabilities were found but annual survival rates for young adult frogs
has been estimated to be between 55% (Fog and Hesselsøe 2009) and 63% (Loman 1984).
These rates are not habitat specific but are realized during annual movements in a heterogeneous
landscape.
All land cover categories in GIS maps were ranked according to amphibian survivability
by specialist and assigned a value <strong>of</strong> relative survival index (H s ) (Table A2) which is subsequently
converted into daily survival probabilities (D s ). The parameter set (σ 0 , σ 1 ) gives <strong>the</strong>
functional relationship between H s and D s . The parameters were found by iteration. The
model was run with varying combinations <strong>of</strong> parameter values on both test maps until a set
was found with which <strong>the</strong> annual survival rates were within 55% and 63%. With <strong>the</strong> chosen
parameter set <strong>the</strong> realized annual survival rates was between 56 % and 57 % in both maps.
Table A4 shows <strong>the</strong> resulting habitat specific daily survival probability.
Road survival
Hels and Buchwald (2001, fig. 5) found <strong>the</strong> probability <strong>of</strong> a Moor frog getting killed when
crossing a road ranged from ca 35% to ca 90% depending on traffic intensity. We assume
traffic intensity to be correlated with road width and let daily survival probability (D s ) depend
on road category as shown in Table A5.
88

Chapter Two
References
Dunning JB, Danielson BJ, Pulliam HR (1992) Ecological processes that affect populations in
complex landscapes. Oikos 65: 169-175. doi:10.2307/3544901
Eigenbrod F, Hecnar SJ, Fahrig L (2008) Accessible habitat: an improved measure <strong>of</strong> <strong>the</strong> effects
<strong>of</strong> habitat loss and <strong>roads</strong> on wildlife populations. Landscape Ecology 23: 159-168.
doi:10.1007/s10980-007-9174-7
Fog K, Hesselsøe M (2009) Udvikling af prototypemodel til brug for forvaltning af
spidssnudet frø i forbindelse med vejanlæg. Amphi Consult, pp.
Hartung H (1991) Untersuchung zur terrestrischen Biologie von Populationen des Moorfrosches
(Rana arvalis NILSSON 1842) unter besonderer Berücksichtigung der Jahresmobilität.
Hamburg: Universität Hamburg.
Hels T, Buchwald E (2001) The effect <strong>of</strong> road kills on amphibian populations. Biological
Conservation 99: 331-340. doi:10.1016/S0006-3207(00)00215-9
Loman J (1984) Density and survival <strong>of</strong> Rana arvalis and Rana temporaria. Alytes 3: 125-
134
Mazerolle MJ, Desrochers A (2005) Landscape resistance to frog movements. Canadian Journal
<strong>of</strong> Zoology-Revue Canadienne De Zoologie 83: 455-464. doi:10.1139/z05-032
Pontoppidan M-B, Nachman G (In review) Effects <strong>of</strong> within-patch heterogeneity on connectivity
in pond-breeding amphibians studied by means <strong>of</strong> an individual-based model. Webecology:
Pope SE, Fahrig L, Merriam NG (2000) Landscape complementation and metapopulation
effects on leopard frog populations. Ecology 81: 2498-2508
Tramontano R (1997) Continuous radio tracking <strong>of</strong> <strong>the</strong> common frog, Rana temporaria. Herpetologia
Bonnensis: 359-365
89

Chapter Two
Tables & Figures
Table A1. List <strong>of</strong> parameters, <strong>the</strong>ir default values and <strong>the</strong> procedure in which <strong>the</strong>y appear.
Parameter Value
Procedure
ν 0 1.50E-06 Settle
ν 1 0.06 Settle
σ 0 2.2 Map-scan
σ 1 4 Map-scan
c 7 Move
s 0.5 Move
90

Chapter Two
Table A2. 3 Land cover categories and <strong>the</strong> associated values <strong>of</strong> Habitat survival, Habitat attraction
and Summer quality
Habitat Code
(H c )
Description
Habitat
Attraction
(H a )
Habitat
Survival
(H s )
2 4-lane motorway 2 N/A 1
Summer
Quality
(H q )
3 2-lane motorway 2 N/A 1
4 Road, width > 6m 3 N/A 1
5 Road, width 3-6 m 3 N/A 1
6 O<strong>the</strong>r <strong>roads</strong> 3 2 2
8 Pathway 4 4 3
11 Multiple surface 3 3 3
11 Railway 4 2 3
12 Building 1 N/A N/A
15 O<strong>the</strong>r made surface 2 3 2
18 Wetlands 5 5 5
20 Running water 4 4 3
22 Meadows 5 5 5
24 Grassland 4 4 4
25 Lakes 1 N/A N/A
28 Hedgerow 4 4 4
29 Heath land 5 5 4
32 Woodland 4 4 4
34 Stand <strong>of</strong> trees 4 4 3
36 Bare surface 2 2 1
40 Fallow land 4 4 4
42 Field crops 2 2 2
91

Chapter Two
Table A3 Observed patterns and <strong>the</strong> patterns emerging using three different expressions with
H a entering into <strong>the</strong> Move procedure as well as random movement. Results are shown for two
different maps, Kalundborg (KaB) and Holstebro (HoB)
Pattern
Ratio between frog
densities in good
and bad habitat
(Hartung 1991)
Percentage <strong>of</strong> individual
choosing
good habitat (Mazerolle
and Desrochers
2005)
Random H a
2
H a exp(H a )
Observed
KaB HoB KaB HoB KaB HoB KaB HoB
0.29 0.39 0.48 0.46 0.64 0.43 0.53 0.38 0.46
72% 72% 67% 68% 61% 70% 66% 73% 68%
Table A4 Habitat survival index (H s ), <strong>the</strong> corresponding daily survival probability (D s ) and D s
converted into annual survival probability.
H s
D s
Annual survival
probability
1 0.9820 0.01
2 0.9960 0.38
3 0.9984 0.68
4 0.9991 0.81
5 0.9995 0.88
92

Chapter Two
Table A5 Road categories with <strong>the</strong> corresponding habitat code (H c ) and daily survival probability
(D s )
Habitat code (H c ) Road category
D s
2 4-lane motorway 0.1
3 2-lane motorway 0.2
4
5
Road width > 6
m
Road width 3-6
m
0.5
0.8
Figure A1 Illustration <strong>of</strong> how accessible summer habitat is identified.
Blue circle is a pond; dotted circle represents maximum migration distance. Green areas are
accessible summer habitat while shaded areas are inaccessible summer habitat.
a) All summer habitat within migration distance is regarded as accessible
b) Road traversing <strong>the</strong> habitat prevents access to summer habitat on <strong>the</strong> opposite side <strong>of</strong> <strong>the</strong>
road
c) Structures breaking <strong>the</strong> road such as underpasses again permit access to summer habitat on
<strong>the</strong> opposite side <strong>of</strong> <strong>the</strong> road.
a b c
93

Chapter Two
Figure A2 Settling probability.
If a frog agent encounters a summer habitat cell, <strong>the</strong> probability <strong>of</strong> settling in <strong>the</strong> cell will depend
on <strong>the</strong> time, measured as day number
1.0
0.8
Settle probability
0.6
0.4
0.2
0.0
170 190 210 230 250 270 290 310
Daynumber
Figure A3 Dispersal distances
The frequency distribution <strong>of</strong> dispersal distances with chosen settle-parameters for a) HoB
map b) KaB map. Black line shows accumulated frequencies.
a
b
25
25
20
20
%
15
%
15
10
10
5
5
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Mor
Dispersal distance (km)
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Mor
Dispersal distance (km)
94

CHAPTER THREE
SAIA – A MANAGEMENT TOOL FOR
ASSESSMENT OF ROAD EFFECTS ON
REGIONAL POPULATIONS OF
MOOR FROGS (RANA ARVALIS)
Submitted to Nature Conservation
December 2012

Chapter Three
SAIA – a management tool for assessment <strong>of</strong> road
effects on regional populations <strong>of</strong> Moor frogs (Rana
arvalis)
Maj-Britt Pontoppidan, Gösta Nachman
Both:
Section for Ecology and Evolution
Department <strong>of</strong> Biology
University <strong>of</strong> Copenhagen
Universitetsparken 15
DK-2100 Copenhagen
Corresponding author:
M-B. Pontoppidan
email: mbp@bio.ku.dk
phone: +45 51518791
97

Chapter Three
Abstract
An expanding network <strong>of</strong> <strong>roads</strong> and railways fragments natural habitat affecting <strong>the</strong> amount
and quality <strong>of</strong> habitat and reducing connectivity between habitat patches with severe consequences
for biodiversity and population persistence. To ensure an ecologically sustainable
transportation system it is essential to find agreement between nature conservation and land
use. GIS are frequently used to support management decisions in landscape planning. They
are used to produce land-use maps and provide various tools for measuring connectivity etc.,
mostly based on graph <strong>the</strong>ory or least cost analysis considering distances and landscape permeability.
However, GIS map do not provide information about <strong>the</strong> particular dispersal, survival
and establishment <strong>of</strong> <strong>the</strong> animals, which depend not only on <strong>the</strong> quality <strong>of</strong> <strong>the</strong> habitat
but also on <strong>the</strong> behaviour <strong>of</strong> <strong>the</strong> animals, <strong>the</strong>ir response to habitat conditions and landscape
elements. Individual based modelling has been proven to be suitable for describing such processes.
The study presented, combines GIS with IBM in order to merge <strong>the</strong> strengths <strong>of</strong> both
approaches, since a combination <strong>of</strong> land use analysis with animal behaviour is essential for an
effective planning <strong>of</strong> landscapes, providing for <strong>the</strong> urban use by humans as well as <strong>the</strong> survival
<strong>of</strong> endangered species. The model, called SAIA (Spatial Amphibian Impact Assessment),
provides information on connectivity as well as estimates <strong>of</strong> population persistence. By
means <strong>of</strong> a case study dedicated to pond breeding amphibians (Rana arvalis) we demonstrate
how SAIA can be used for assessing which management measures would be best to mitigate
<strong>the</strong> effect <strong>of</strong> landscape fragmentation caused by road constructions.
98

Chapter Three
Introduction
Over <strong>the</strong> last decade a growing amount <strong>of</strong> literature has documented <strong>the</strong> severe <strong>impact</strong>s <strong>of</strong>
transport infrastructure on biodiversity, population persistence and gene flow. An expanding
network <strong>of</strong> <strong>roads</strong> and railways divides natural habitat into smaller and smaller fragments, affecting
<strong>the</strong> amount and quality <strong>of</strong> habitat and reducing connectivity between habitat patches
(C<strong>of</strong>fin 2007; Fahrig and Rytwinski 2009; Forman and Alexander 1998; Holderegger and Di
Giulio 2010; Spellerberg 1998; Trombulak and Frissell 2000). To ensure an ecologically sustainable
transportation system it is essential to find agreement between nature conservation
and land use. In Europe and <strong>the</strong> US, programs and policies are being developed addressing
this need in strategic and environmental <strong>impact</strong> assessments (Brown 2006; Iuell et al. 2003;
Trocmé et al. 2003), However, sustainable road planning requires adequate tools for assessment,
prevention and mitigation <strong>of</strong> <strong>the</strong> <strong>impact</strong>s <strong>of</strong> infrastructure (Beckmann 2010; Forman et
al. 2003; Gontier et al. 2010).
The persistence <strong>of</strong> a population depends on <strong>the</strong> amount and accessibility <strong>of</strong> its required
resources and, within a metapopulation framework, also on sufficient dispersal between subpopulations
(Dunning et al. 1992; Wiens 1997). Therefore, measures <strong>of</strong> connectivity have
been used as indicators <strong>of</strong> a landscape’s capability to sustain a population. Likewise, GIS has
proved to be an important tool when assessing <strong>the</strong> <strong>impact</strong> <strong>of</strong> <strong>roads</strong> on landscape fragmentation
and/or connectivity (Beckmann 2010; Brown 2006; Calabrese and Fagan 2004). Different
species have both different habitat requirements and behaviours. Therefore, connectivity must
in essence be species specific. Methods using least cost modelling (Adriaensen et al. 2003;
Epps et al. 2007) or graph <strong>the</strong>oretical approaches (Bunn et al. 2000; Minor and Urban 2008;
Zetterberg et al. 2010) usually combine GIS data with some species specific data such as dispersal
distances or habitat suitability. However, nei<strong>the</strong>r <strong>of</strong> <strong>the</strong>se methods considers <strong>the</strong> particular
dispersal, survival and establishment <strong>of</strong> <strong>the</strong> animals, which depend not only on <strong>the</strong>
quality <strong>of</strong> <strong>the</strong> habitat but also on <strong>the</strong> behaviour <strong>of</strong> <strong>the</strong> animals, <strong>the</strong>ir responses to habitat conditions,
landscape elements, interactions with o<strong>the</strong>r animals and many o<strong>the</strong>r factors. Individual
based models (IBMs) have proved to be suitable for describing such processes (Grimm
1999; McLane et al. 2011) and recently <strong>the</strong>re has been an increase in IBM case studies demonstrating
<strong>the</strong> potential for analysing population dynamics emerging from <strong>the</strong> interactions
99

Chapter Three
between landscape settings and animal behaviour (e.g. Graf et al. 2007; Kramer-Schadt et al.
2004; Pe'er et al. 2011).
We have developed a strategic management tool to be used in assessment and mitigation
<strong>of</strong> road effects on a regional population <strong>of</strong> pond-breeding amphibians. The model, called
SAIA (Spatial Amphibian Impact Assessment), combines <strong>the</strong> use <strong>of</strong> GIS land cover maps
with IBM and provides information on connectivity as well as estimates <strong>of</strong> population persistence.
SAIA is to be used by <strong>the</strong> Danish road authorities when assessing how new road construction
may affect Moor frogs (Rana arvalis). In this paper we demonstrate how SAIA can
be used for assessing which management measures would be best to mitigate <strong>the</strong> effect <strong>of</strong>
landscape fragmentation caused by <strong>the</strong> construction <strong>of</strong> a road ca 90 km west <strong>of</strong> Copenhagen,
Denmark. To achieve this goal <strong>the</strong> following specific research questions were addressed:
What is <strong>the</strong> structure <strong>of</strong> <strong>the</strong> regional habitat network before road construction
How is <strong>the</strong> habitat network affected by <strong>the</strong> new road
Which mitigation strategies are best suited to preserve <strong>the</strong> overall persistence <strong>of</strong> <strong>the</strong> regional
population <strong>of</strong> Moor frogs
Methods
SAIA combines an individual based model with a population based model. The IBM is basically
identical to <strong>the</strong> model described in Pontoppidan and Nachman (In prep.) It simulates <strong>the</strong>
movement <strong>of</strong> newly metamorphosed frogs from <strong>the</strong>ir natal ponds to new habitat patches.
Here, we use <strong>the</strong> terms dispersal and migration as defined by Semlitsch (2008), i.e. dispersal
is interpopulational, unidirectional movements from natal sites to o<strong>the</strong>r breeding sites and
migration is intrapopulational, round-trip movements toward and away from aquatic breeding
sites. The habitat <strong>of</strong> pond breeding amphibians, such as <strong>the</strong> Moor frog, includes terrestrial as
well as aquatic habitat. Therefore, we define an adequate habitat patch <strong>of</strong> a subpopulation as
containing not only <strong>the</strong> breeding pond but also all accessible summer habitat within migration
distance from <strong>the</strong> pond (Dunning et al. 1992; Pontoppidan and Nachman In review; Pope et
al. 2000).
100

Chapter Three
Model species
Moor frogs spend most <strong>of</strong> <strong>the</strong>ir life in terrestrial habitat; aquatic habitat is only used during
<strong>the</strong> breeding season in early spring (Elmberg 2008; Glandt 2008; Hartung 1991). Soon after
breeding, <strong>the</strong> frogs return to <strong>the</strong> summer habitat, which lies mostly within a 400 m radius
from <strong>the</strong> breeding pond (Elmberg 2008; Hartung 1991; Kovar et al. 2009). Adult frogs show
strong site fidelity and <strong>of</strong>ten use <strong>the</strong> same breeding pond and summer habitat from year to
year (Loman 1994). Long distance dispersal takes place predominantly during <strong>the</strong> juvenile
life-stage (Semlitsch 2008; Sinsch 1990; 2006). Shortly after metamorphosis, <strong>the</strong> young frogs
leave <strong>the</strong> natal pond and disperse into <strong>the</strong> surrounding landscape seeking suitable summer
habitat. Dispersal distances are between a few hundred meters up to 1-2 kilometres (Baker
and Halliday 1999; Hartung 1991; Sinsch 2006; Vos and Chardon 1998). The juveniles stay
in terrestrial habitat 2-3 years until <strong>the</strong>y reach maturity, although some observations indicate
that juvenile frogs follow <strong>the</strong> adults during <strong>the</strong> spring migration, without entering <strong>the</strong> breeding
ponds (Hartung 1991; Sjögren-Gulve 1998) .
Model overview
As in its predecessor (Pontoppidan and Nachman In prep.), SAIA is based on a GIS raster
map. Each raster cell contains information about <strong>the</strong> cell’s land cover or habitat type (H c ) and
relative suitability as summer habitat (H q ), its relative attraction to frogs during movement
(H a ) and <strong>the</strong> relative survival index (Hs) associated with <strong>the</strong> cell. A point-data set containing
information on potential breeding ponds was obtained from extensive field surveys in <strong>the</strong>
area. Each pond is characterized by an ID-number, <strong>the</strong> perimeter <strong>of</strong> <strong>the</strong> pond (O), <strong>the</strong> number
<strong>of</strong> egg masses found during <strong>the</strong> field surveys (N 0 ) and a quality index (Q).
The GIS map is imported into <strong>the</strong> model and <strong>the</strong> model landscape is constructed. The
point-data set is used to create stationary pond agents. After import, <strong>the</strong> map is processed and
additional variables are added to <strong>the</strong> raster cells and pond agents. Daily survival probabilities
(D s ) associated with each cell are computed based on <strong>the</strong> cell values for HabitatCode and
HabitatSurvival. Cells with high values <strong>of</strong> SummerQuality are classified as summer habitat.
Summer habitat cells can be completely surrounded by o<strong>the</strong>r summer habitat cells (core cells)
or have one or more neighbouring cells which are not summer habitat (edge cells). To account
for edge effects, core cells are given <strong>the</strong> area value (W) <strong>of</strong> 1 while W is 0.5 for edge cells
(Watts and Handley 2010). Pond agents are updated with <strong>the</strong> summer habitat cells within mi-
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Chapter Three
gration distance (A) as well as with <strong>the</strong> effective area <strong>of</strong> <strong>the</strong> summer habitat (A´). The carrying
capacity <strong>of</strong> <strong>the</strong> summer habitat (K) is estimated, based on <strong>the</strong> amount <strong>of</strong> available summer
habitat and number <strong>of</strong> egg masses found during field work. Table 1 shows a full list <strong>of</strong> model
variables.
At <strong>the</strong> start <strong>of</strong> a simulation 250 frog agents are created in each pond agent. The frogs
disperse through <strong>the</strong> landscape in random directions from <strong>the</strong> ponds; <strong>the</strong> movement <strong>of</strong> <strong>the</strong>
frogs depends on <strong>the</strong> attractiveness <strong>of</strong> neighbouring cells and <strong>the</strong> cells’ suitabilities as summer
habitat. Survival probabilities depend on <strong>the</strong> traversed habitat types. Unlike <strong>the</strong> former model,
movement behaviour in SAIA also depends on wea<strong>the</strong>r conditions. When daily precipitation
exceeds a given threshold (α), <strong>the</strong> variables HabitatAttraction and DailySurvival <strong>of</strong> all accessible
cells are given <strong>the</strong> highest value. An exception is paved <strong>roads</strong> where only HabitatAttraction,
but not DailySurvival, is changed. After <strong>the</strong> simulation, immigration probabilities between
all pairs <strong>of</strong> subpopulations are calculated and an immigration matrix is constructed. The
immigration matrix is used to compute connectivity. Apart from being a landscape attribute in
itself, <strong>the</strong> matrix also enters into to <strong>the</strong> population-based procedure PopulationDynamics
(PD).
The PD-procedure estimates population sizes in each pond through 40 iterations <strong>of</strong> a life
cycle model. The elements <strong>of</strong> <strong>the</strong> life cycle model are 1) Reproduction, 2) Survival and 3)
Immigration. For simplicity, we only look at <strong>the</strong> female part <strong>of</strong> <strong>the</strong> population. We assume a
sex ratio <strong>of</strong> 0.5 and that females always become mated. Pond subpopulations are grouped by
age from 0 through 6 years, and survival and reproductive rates come from life-table data
constructed by amphibian experts (Table 2). The number <strong>of</strong> egg masses found in <strong>the</strong> surveyed
ponds (N 0 ) is expected to equal <strong>the</strong> number <strong>of</strong> breeding females in <strong>the</strong> subpopulation. This
number is set as <strong>the</strong> initial population size <strong>of</strong> <strong>the</strong> pond. After each iteration, <strong>the</strong> pond variables
Froglets and AgeClassList are updated with <strong>the</strong> reproductive output and <strong>the</strong> number <strong>of</strong> surviving
individuals in each age class, respectively. The number <strong>of</strong> immigrants is added to age
class 0 in <strong>the</strong> AgeClassList.
Individuals can reproduce starting in age 3. As in Hels and Nachman (2002), <strong>the</strong> expected
egg production <strong>of</strong> a female is assumed to follow a negative binomial distribution with
mean and clumping parameter k. is <strong>the</strong> mean number <strong>of</strong> eggs produced by a female <strong>of</strong> a
given age. The number <strong>of</strong> newly metamorphosed frogs, ready to disperse is considered as <strong>the</strong>
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reproductive output. This involves <strong>the</strong> survival <strong>of</strong> egg and larvae, as well as <strong>the</strong> survival <strong>of</strong> <strong>the</strong>
young frogs <strong>the</strong> first two weeks after metamorphosis. The overall probability that an egg develops
into a frog that survives until dispersal time is assumed to be affected by two factors:
Density <strong>of</strong> eggs in <strong>the</strong> pond and <strong>the</strong> quality <strong>of</strong> <strong>the</strong> pond. The conditional probability that a
frog survives from age a to age a+1 is assumed to depend on age. Fur<strong>the</strong>rmore, survival is
assumed to depend on <strong>the</strong> frog density in <strong>the</strong> summer habitat. For simplicity, this is modelled
as a “culling” process when frog density exceeds <strong>the</strong> carrying capacity <strong>of</strong> summer habitat.
Immigration probabilities between all pairs <strong>of</strong> subpopulations are obtained from <strong>the</strong> immigration
matrix. The actual number <strong>of</strong> immigrants a subpopulation receives depends on <strong>the</strong> variable
Froglets <strong>of</strong> each <strong>of</strong> <strong>the</strong> o<strong>the</strong>r ponds and <strong>the</strong> corresponding immigration probability. Emigration
rates are not modelled explicitly. For a full model description according to <strong>the</strong> protocol
suggested by Grimm et al. (2006); (2010) see Appendix 1 in supplementary material and
Pontoppidan and Nachman (In prep.). Netlogo v.4.1.3 (Wilensky 1999) was used as modelling
environment (freely downloadable at http://ccl.northwestern.edu/netlogo).
Output
At <strong>the</strong> end <strong>of</strong> a simulation, <strong>the</strong> following output was recorded: <strong>the</strong> number <strong>of</strong> surviving frogs,
<strong>the</strong> natal and breeding ponds <strong>of</strong> all frogs, and <strong>the</strong> immigration probabilities (p ij ) between all
pair-wise ponds. Landscape connectivity (S) is found as
∑ ∑
, . (Eq. 1)
By <strong>the</strong> end <strong>of</strong> <strong>the</strong> PD-procedure, <strong>the</strong> population size <strong>of</strong> each pond is estimated as <strong>the</strong> resulting
numbers <strong>of</strong> frogs <strong>of</strong> ages 2 through 6. The model was run 50 times and mean connectivity
with 95% confidence interval (CI) were computed. For each pond, as well as for <strong>the</strong> whole
landscape, we computed mean population size with 95% confidence intervals (CI) and <strong>the</strong>
proportion <strong>of</strong> replicates where <strong>the</strong> predicted population size was positive. Mean number <strong>of</strong>
populated ponds with 95% CI was also calculated.
Ponds were grouped into clusters depending on <strong>the</strong>ir mutual connectivity, using unweighted,
arithmetic, average clustering as described by Legendre and Legendre (1998).
Since immigration probabilities between ponds are not necessarily symmetric, i.e. p ij ≠ p ji , we
used summed immigrations probabilities as similarity measures (m), i.e. m ij = p ij + p ji . The
threshold at which a given pond or cluster no longer can be added to ano<strong>the</strong>r cluster was set to
m ij ≤ 0.01. Connectivity between any pairs <strong>of</strong> clusters (S k,l ) is found as
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Chapter Three
, ∑ ∑
,
(Eq. 2)
where n k and n l are <strong>the</strong> number <strong>of</strong> ponds in clusters k and l, respectively.
Scenarios
We constructed five different scenarios. The analyses <strong>of</strong> scenario 0 and scenario 1 were used
to plan a series <strong>of</strong> suggestions for mitigation measures which are put into effect in scenarios 2,
3a and 3b.
Scenario 0: Before <strong>the</strong> road project
This is an analysis <strong>of</strong> <strong>the</strong> landscape before <strong>the</strong> planned road construction and it works as a
reference against which <strong>the</strong> o<strong>the</strong>r analyses are compared. As input data we use a GIS data set
from a road project in Denmark, supplied by <strong>the</strong> Danish Road Directorate and Amphi Consult.
The project concerns an area in <strong>the</strong> north-western part <strong>of</strong> Zealand, 10 km east <strong>of</strong> <strong>the</strong> city
<strong>of</strong> Kalundborg (55° 40.14’ N 11° 17.85’ E) (fig. 1). All cell values <strong>of</strong> H a , H s and H q are
ranked on a scale from 1-5, following <strong>the</strong> protocol <strong>of</strong> Hassingboe et al. (2012) (Table 3). The
extent <strong>of</strong> <strong>the</strong> map is 600 x 800 cells, and each cell is 10 x 10 m. The point data set contains
information about potential breeding ponds found during <strong>the</strong> field survey. Pond qualities (Q)
range from 0.1 – 1 and relate to <strong>the</strong> suitability <strong>of</strong> <strong>the</strong> pond and <strong>the</strong> immediate surroundings in
regard to egg and larval survival. These values were based on field work conducted by amphibian
experts. The data set contains 121 ponds, <strong>of</strong> which 23 ponds are <strong>of</strong> high quality (Q >
0.6). In total, 106 egg masses were found distributed among 6 ponds (Fig. 2A).
Scenario 1: After <strong>the</strong> road project
The landscape in scenario 0 is modified according to <strong>the</strong> planned road project. The changes
include a broadening <strong>of</strong> an existing 2-lane motorway into a 4-lane motorway as well as an
extension <strong>of</strong> <strong>the</strong> motorway. This changes <strong>the</strong> survival parameter Ds <strong>of</strong> <strong>the</strong> road from 0.20 to
0.10. The construction involves removal <strong>of</strong> five ponds along <strong>the</strong> road (Fig 3A).
Scenario 2: Construction <strong>of</strong> underpasses and drift fences
Three underpasses are added to scenario 1. Drift fences are established along <strong>the</strong> road for 100
m on each side <strong>of</strong> <strong>the</strong> underpass, except for underpass 2 which has a 300 m drift fence to <strong>the</strong>
south (Fig 4A).
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Chapter Three
Scenario 3: Construction <strong>of</strong> artificial breeding ponds
Eight new breeding ponds are added to scenario 1. Each breeding pond is assigned a pond
quality <strong>of</strong> 0.7. Scenarios 3a and 3b represent two alternative locations <strong>of</strong> <strong>the</strong> eight ponds (Fig
4B and C).
Results
Initial analyses
Scenario 0
The average proportion <strong>of</strong> ponds populated during a simulation was 32%, although only 22%
<strong>of</strong> <strong>the</strong> ponds have a more permanent status (pond persistence probability > 0.75). The abundance
<strong>of</strong> adult female frogs was estimated to be 157; annual survival probability is 57%, and
landscape connectivity was 55 (Fig 5).
The cluster analysis identified 13 clusters, cluster sizes ranging from 2-20 ponds (Fig
2B, Table 4). The six populated ponds found during field surveys were distributed on four
different clusters. One pond with only one adult female was found in cluster 5 (c5). Ano<strong>the</strong>r
pond belongs to c4 and two o<strong>the</strong>r ponds are found in c8. In each <strong>of</strong> <strong>the</strong>se ponds, <strong>the</strong> initial
population size was set to 5 adult females. Cluster c11 contains <strong>the</strong> remaining two populated
ponds with an initial total population <strong>of</strong> 90 adult females. Apart from c5, all <strong>of</strong> <strong>the</strong>se initially
populated clusters exhibited high viability. Clusters c4, c8 and c11 have mean pond persistence
probabilities between 77% - 93% and estimated cluster abundances from 23-51 adult
females. Cluster c9 also shows high values <strong>of</strong> abundance and persistence. Although initially
unpopulated, c9 contains several high quality ponds and is connected with c8 and c11 which
may promote colonisation and establishment. In c6 and c7, <strong>the</strong> mean pond persistence probability
is considerably lower (29-35%) as is <strong>the</strong> estimated cluster abundance. While <strong>the</strong> two
clusters, especially c6, are connected with o<strong>the</strong>r populated clusters, <strong>the</strong>y lack high -quality
ponds and <strong>the</strong> clusters may function as sinks. In <strong>the</strong> remaining clusters <strong>the</strong> estimated abundance
is less than one individual.
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Chapter Three
Scenario 1
After construction <strong>of</strong> <strong>the</strong> road, <strong>the</strong> proportion <strong>of</strong> populated ponds was reduced to 26% and
permanent ponds are now down to 16%. Annual survival rate is 56% and estimated abundance
is 136 adult females. Landscape connectivity decreased to 51 (Fig 5).
The number <strong>of</strong> clusters was unchanged but connectivity between clusters was reduced
(Table 5). Connectivity from c7 and c9 to <strong>the</strong>ir primary source (c8) decreased more than 80%.
Moreover, three ponds were lost in c7 and c9 due to <strong>the</strong> road construction. Estimated abundance
and mean pond persistence probability decreased in c7 and c9 and <strong>the</strong>se clusters were
no longer able to uphold viable populations (fig 3B). However <strong>the</strong> initially populated clusters
c4, c8 and c11 were not affected by <strong>the</strong> road construction.
Mitigation planning
The first analyses revealed that <strong>the</strong> landscape contains three viable populations (c4, c8 & c11)
centred on <strong>the</strong> initially populated ponds. These populations appear not to be affected by <strong>the</strong>
road construction and in <strong>the</strong> simulations <strong>the</strong> clusters seemed to function as sources enabling
colonisation and establishment <strong>of</strong> populations in c9 and c7. Cluster c4 has a large and viable
population, but even though it is well connected with <strong>the</strong> neighbouring clusters <strong>the</strong>ir qualities
were not high enough to enable establishment <strong>of</strong> new populations. Since c4 is not connected
with c7 and c9, its potential as source cluster is low. Cluster c8 seems to be <strong>the</strong> primary
source cluster to c9 and c7; however, expansion <strong>of</strong> <strong>the</strong> road heavily reduces its value as a
source. Fur<strong>the</strong>rmore, <strong>the</strong> removal <strong>of</strong> three ponds between c9 and c7 may diminish <strong>the</strong> connectivity
between <strong>the</strong>se clusters. Cluster c11 has a viable population and although situated somewhat
remotely <strong>the</strong>re is still some connectivity to c7 and c9.
The results indicate that, in order to compensate or mitigate <strong>the</strong> effect <strong>of</strong> <strong>the</strong> road project,
<strong>the</strong> best strategies will be ei<strong>the</strong>r to re-establish connectivity across <strong>the</strong> road between c8
and c7/c9 and between c7 and c9 or to take advantage <strong>of</strong> <strong>the</strong> viability <strong>of</strong> c11 and its source
potential. Based on this, we created and analysed <strong>the</strong> following scenarios:
Scenario 2: Connectivity across <strong>the</strong> road is re-established by constructing three underpasses
and drift fences along <strong>the</strong> middle section <strong>of</strong> <strong>the</strong> motorway (Fig. 4A). The expectation is
that connectivity between c8 and c9/c7 will improve and enable establishment <strong>of</strong> populations
in c9.
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Chapter Three
Scenario 3a: The quality <strong>of</strong> c9 and c11 is improved by establishing three, and <strong>the</strong>n five,
new high -quality ponds within <strong>the</strong> range <strong>of</strong> <strong>the</strong> clusters (Fig. 4B). The three new ponds in c9
are expected to improve <strong>the</strong> probability <strong>of</strong> successful establishment <strong>of</strong> immigrants as well as
reconnect c9 with c7.We expected an increase in abundance in c11, and hence increased immigration
to and colonisation <strong>of</strong> c9.
Scenario 3b: This is a modification <strong>of</strong> scenario 3a. The quality <strong>of</strong> c9 and c11 is still improved
but with only one and two ponds, respectively. The remaining five ponds are used to
create a dispersal corridor between c11 and c9 (Fig. 4C). This strategy is expected to enhance
<strong>the</strong> abundance in c11 and to improve connectivity to c9, <strong>the</strong>reby increasing <strong>the</strong> probability <strong>of</strong>
colonisation.
Mitigation analyses
Scenario 2
Quite unexpectedly, <strong>the</strong> creation <strong>of</strong> drift fences and underpasses did not improve <strong>the</strong> condition
<strong>of</strong> <strong>the</strong> landscape. The mean proportion <strong>of</strong> populated ponds is 26% and permanent ponds is
16% as in scenario 1. However, <strong>the</strong> estimated abundance <strong>of</strong> female adults decreased to 115,
landscape connectivity is 48 and annual survival rate 53% (Fig. 5).
Two <strong>of</strong> <strong>the</strong> underpasses (including drift fences) were placed between c6 and c7; <strong>the</strong>
third between c8 and c9. As expected, connectivity between c8 and 9 was greatly improved.
Cluster c9 now spans <strong>the</strong> road and it annexed one <strong>of</strong> <strong>the</strong> ponds in <strong>the</strong> periphery <strong>of</strong> c8 (Fig.
4A). Abundance and mean pond persistence probability <strong>of</strong> c9 increased; this, however, was
due to <strong>the</strong> inclusion <strong>of</strong> a pond from c8. Persistence and abundance did not improve on <strong>the</strong>
original configuration <strong>of</strong> c9 (Table 6). Apart from c9, connectivity between initially populated
clusters and o<strong>the</strong>r clusters did not improve. Connectivity to c4 and c11 were unchanged, while
connectivity to c8 actually decreased. Finally, <strong>the</strong> abundance <strong>of</strong> frogs in c4 and c11 decreased
to 20% even though connectivity both within <strong>the</strong> cluster and to o<strong>the</strong>r clusters was unchanged.
Scenario 3a
Establishment <strong>of</strong> eight new ponds had a positive effect on landscape condition. The estimated
number <strong>of</strong> adult females increased to 143, proportion <strong>of</strong> populated ponds is 31%, <strong>of</strong> which
19% are permanently populated. Landscape connectivity is 56 and annual survival rate 56%
(Fig. 5).
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Chapter Three
The five new ponds in c11 performed well and contained permanent populations. However,
<strong>the</strong> performance <strong>of</strong> <strong>the</strong> cluster did not improve, apart from a slightly higher persistence
probability (Table 6). Cluster c9 seemed to benefit from <strong>the</strong> additional ponds, although none
<strong>of</strong> <strong>the</strong> new ponds contained permanent populations. Cluster abundance and connectivity were
nearly restored to <strong>the</strong>ir original conditions although mean pond persistence probability was
still below 50%. Connectivity from c7 to o<strong>the</strong>r ponds improved somewhat, but not enough to
restore <strong>the</strong> cluster to its former performance (Fig. 4B).
Scenarios 3b
With this strategy we succeeded in restoring <strong>the</strong> landscape to its original ecological performance.
The number <strong>of</strong> adult female frogs is 159. Mean proportion <strong>of</strong> populated ponds is 32%
and 22% are populated permanently. Annual survival rate is 56% and landscape connectivity
is 55 (Fig. 5).
Three <strong>of</strong> <strong>the</strong> new ponds are now part <strong>of</strong> c9 while <strong>the</strong> remaining five new ponds belong
to c11. Connectivity between c9 and c11 is strong and six <strong>of</strong> <strong>the</strong> new ponds contain permanent
populations (Fig. 4C). The abundance and mean persistence probability <strong>of</strong> c11 increased
and are now better than before <strong>the</strong> road construction. Conditions in c9 also improved, compared
to scenario 1, but its original performance in not quite restored. The performance <strong>of</strong> c7
did not change and is still at <strong>the</strong> same level as found in scenario 1 (Table 6).
Discussion
This study demonstrates how initial analyses <strong>of</strong> <strong>the</strong> landscape before and after <strong>the</strong> planned
road constructions can help identify which areas will be most affected by construction. The
analysis enables <strong>the</strong> user to recognise <strong>the</strong> colonisation potential <strong>of</strong> <strong>the</strong> clusters and to identify
source or sink clusters and to use this knowledge for planning mitigation measures. In <strong>the</strong>
present case study, <strong>the</strong> simulations indicated that <strong>the</strong> population recorded during <strong>the</strong> field survey
will be largely unaffected. Never<strong>the</strong>less, <strong>the</strong> road construction will severely impair <strong>the</strong>
colonisation potential <strong>of</strong> cluster c8, <strong>the</strong>reby reducing <strong>the</strong> ecological performance <strong>of</strong> <strong>the</strong> landscape.
Of <strong>the</strong> three mitigation strategies tested, <strong>the</strong> analysis shows that scenario 3b is <strong>the</strong> best
solution. This strategy <strong>of</strong> connecting clusters c9 and c11 restores <strong>the</strong> landscape to its former
ecological performance. Even though not all individual ponds or clusters would be in <strong>the</strong>
same condition as before, <strong>the</strong> strategy promotes viable populations on both sides <strong>of</strong> <strong>the</strong> road.
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Chapter Three
The strategy is not strictly aimed at mitigating <strong>the</strong> impaired connectivity across <strong>the</strong> road, but
ra<strong>the</strong>r tries to compensate for <strong>the</strong> effects <strong>of</strong> construction by improving o<strong>the</strong>r areas. Still, <strong>the</strong>
populations on ei<strong>the</strong>r side <strong>of</strong> <strong>the</strong> road are not totally isolated from each o<strong>the</strong>r; some dispersal
does take place making genetic exchange possible.
Comparing <strong>the</strong> results from <strong>the</strong> analyses <strong>of</strong> scenarios 3a and 3b suggests that <strong>the</strong> location
<strong>of</strong> compensating new ponds is not trivial. In both scenarios c11 gets five new ponds, all
<strong>of</strong> high quality. Never<strong>the</strong>less, <strong>the</strong> results differ quite a lot. Scenario 3a places <strong>the</strong> new ponds
within <strong>the</strong> cluster sharing <strong>the</strong> summer habitat <strong>of</strong> o<strong>the</strong>r ponds. Even though <strong>the</strong> new ponds are
colonized and support viable populations, <strong>the</strong> abundance <strong>of</strong> frogs within <strong>the</strong> cluster does not
improve. In scenario 3b, where <strong>the</strong> abundance <strong>of</strong> frogs within cluster c11 increases, <strong>the</strong> new
ponds were placed between c9 and c11 and only partly share summer habitat with o<strong>the</strong>r
ponds. This result emphasizes that for <strong>the</strong> Moor frog <strong>the</strong> carrying capacity <strong>of</strong> an area is not
improved by adding new ponds, only new or better summer habitat can achieve this. Hence,
we may improve cluster performance by creating new ponds in unutilized summer habitat
within dispersal distance.
In scenarios 3a and 3b, c9 is also enlarged with three new ponds. In <strong>the</strong>se cases <strong>the</strong>re
was no difference in frog abundance in <strong>the</strong> cluster whe<strong>the</strong>r <strong>the</strong> new ponds were placed in unused
summer habitat or not. In both scenarios, though, mean pond persistence probability
greatly improved compared to scenario 1. So, while adding ponds to a cluster did not improve
carrying capacity, it ensured a more viable cluster population.
The analysis <strong>of</strong> scenario 2 shows that drift fences and underpasses had negative effects
on <strong>the</strong> ecological performance <strong>of</strong> this landscape. This result is highly surprising as well as
controversial since fences and underpasses are standard mitigation measures used in many
road projects (Iuell et al. 2003). Even though fences and underpasses should prevent road
mortality and promote connectivity, <strong>the</strong> overall annual survival rate, as well as connectivity,
decreased. These effects are probably mostly due to <strong>the</strong> fences. Underpasses per se do not
change movement patterns, but fences do. Moreover, we did see increased connectivity locally
across <strong>the</strong> road between c8 and c9.
Fences may force individuals to move along <strong>the</strong> road exposing <strong>the</strong>m to low quality
habitat for a longer time. Fur<strong>the</strong>rmore, <strong>the</strong> mitigation measures may be counterproductive if
<strong>the</strong> combination <strong>of</strong> fences and underpasses lead individuals into low quality habitat or areas
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Chapter Three
without ponds to colonize. The population dynamics in <strong>the</strong> ponds is an emergent property,
dependent on local conditions as well as regional dynamics. The change in connectivity and
movement patterns caused by <strong>the</strong> migration measures, <strong>the</strong>refore, seems to be able to affect
abundances even in clusters far<strong>the</strong>r away.
Very little is known about <strong>the</strong> effects <strong>of</strong> mitigation measures in general. Once mitigation
measures are implemented, efforts are seldom put into discovering how well <strong>the</strong>y work.
Recordings <strong>of</strong> animals using wild life passages reveal nothing about effects on local and regional
persistence (Lesbarreres and Fahrig 2012). In a simulation study, Jaeger and Fahrig
(2004) found that fencing, while preventing road mortality, did not necessarily improve population
persistence and <strong>the</strong>y recommended fencing only when road mortality is 100 %. In a
study on moose (Alces alces), Olsson and Widen (2008) found that fences resulted in decreased
use <strong>of</strong> wildlife passages. Our simulation results underscore <strong>the</strong> need for a better understanding
<strong>of</strong> how mitigation measures affect animal behaviour and population dynamics.
Conclusion
When planning road constructions, it is important to integrate mitigation measures right from
<strong>the</strong> start. Often <strong>the</strong>re are economic constraints on which measures are possible, certain structures
as viaducts or bridges may already be in place or land available for compensation measures
is restricted. SAIA <strong>of</strong>fers a tool to evaluate different scenarios to find <strong>the</strong> best combination
<strong>of</strong> mitigation measures for a given set <strong>of</strong> conditions. The model is meant to be used by
non-specialists – all that is needed are GIS maps <strong>of</strong> <strong>the</strong> different scenarios. We attempted to
find a balance between detailed and yet intuitive and easy interpretable output. Even though
SAIA was developed for <strong>the</strong> Danish Road Directorate, its use is not restricted to road constructions
but can be applied to o<strong>the</strong>r structures affecting <strong>the</strong> landscape and <strong>the</strong>ir potential
<strong>impact</strong>s on wildlife.
Acknowledgments
The work was funded by <strong>the</strong> Danish Road Directorate. We thank Amphi Consult for providing
us with amphibian expertise and field data. We are grateful for continuous and enthusiastic
feed-back from M. Ujvári, M. Hesselsøe, A. Jørgensen and M. Schneekloth during model
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Chapter Three
development. Special thanks are due to Uta Berger for encouraging and inspiring discussions.
We thank Michal J. Reed for linguistic assistance.
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Chapter Three
Tables
Table 1 List <strong>of</strong> variables characterizing <strong>the</strong> agents in SAIA
Variable
Notation
Value
range
Agent
type
Description
AreaValue W 0.5; 1 Cell Effective area <strong>of</strong> <strong>the</strong> cell
DailySurvival D s Cell Daily survival probability
FrogDensity D Cell Mean number <strong>of</strong> frogs in <strong>the</strong> cell
HabitatAttraction H a 1-5 Cell
The cell’s relative attraction to frogs
during movement
HabitatCode H c Cell The land cover category <strong>of</strong> <strong>the</strong> cell
HabitatSurvival H s 1-5 Cell The cell’s relative survival index
SummerQuality H q 1-5 Cell
The cell’s relative suitability as summer
habitat
BreedingPond Frog Breeding pond <strong>of</strong> frog agents
NatalPond Frog Natal pond <strong>of</strong> frog agents
PondID Pond ID number
PondPerimeter O Pond Perimeter <strong>of</strong> <strong>the</strong> pond
PondQuality Q 0.1-1 Pond Quality index <strong>of</strong> <strong>the</strong> pond
PopulationSize N 0 Pond
SummerHabitat A Pond
SummerHabitatArea A' Pond
Number <strong>of</strong> egg masses found in <strong>the</strong>
pond during survey
Summer habitat cells associated with
<strong>the</strong> pond
Effective area <strong>of</strong> associated summer
habitat
Froglets Pond Number <strong>of</strong> newly metamorphosed frogs
AgeClassList
Pond
Number <strong>of</strong> surviving individuals in age
class 0-6
115

Chapter Three
Table 2 Life table for Rana arvalis and estimated age distribution
Stage/Age Survival probability Fecundity ( eggs pr. female)
Egg/larvae 0.005 - -
0 0.55 0 46.7 %
1 0.55 70 25.7 %
2 0.55 945 14.1%
3 0.55 1190 7.8%
4 0.50 1250 3.9%
5 0.40 1300 1.6 %
6 0.20 1300 0.3%
Percentage <strong>of</strong> population
116

Chapter Three
Table 3 Land cover categories and <strong>the</strong> associated values <strong>of</strong> HabitatSurvival, HabitatAttraction
and SummerQuality
HabitatCode
(H c )
Description
HabitatAttraction
(H a )
HabitatSurvival
(H s )
2 4-lane motorway 2 N/A 1
3 2-lane motorway 2 N/A 1
4 Road, width > 6m 3 N/A 1
5 Road, width 3-6 m 3 N/A 1
6 O<strong>the</strong>r <strong>roads</strong> 3 2 2
8 Pathway 4 4 3
11 Multiple surface 3 3 3
11 Railway 4 2 3
12 Building 1 N/A N/A
15 O<strong>the</strong>r made surface 2 3 2
18 Wetlands 5 5 5
20 Running water 4 4 3
22 Meadows 5 5 5
24 Grassland 4 4 4
25 Lakes 1 N/A N/A
28 Hedgerow 4 4 4
29 Heath land 5 5 4
32 Woodland 4 4 4
34 Stand <strong>of</strong> trees 4 4 3
36 Bare surface 2 2 1
40 Fallow land 4 4 4
42 Field crops 2 2 2
50 Drift fence 1 N/A N/A
60 Underpass 4 4 1
SummerQuality
(H q )
117

Chapter Three
Table 4 Results from analysis <strong>of</strong> scenario 0 (before road construction)
Cluster ID c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
Number <strong>of</strong>
ponds in cluster
Number <strong>of</strong> high
quality ponds
(Q> 0.6)
Connectivity to
o<strong>the</strong>r clusters
Estimated cluster
abundance
Mean pond
persistence
probability
Connectivity to
c4
Connectivity to
c8
Connectivity to
c11
9 5 2 8 20 13 19 7 7 11 12 5 3
2 0 0 4 2 0 1 7 3 0 3 1 0
0.45 0.54 0.30 0.57 2.19 1.13 2.94 0.36 1.20 0.07 0.10 0.05 0.06
0 0 0 49 0 3 11 23 14 0 51 0 0
0 0 0 0.82 0.03 0.29 0.35 0.93 0.73 0.01 0.77 0 0.13
0 0.09 0.04 - 0.01 0.44 0 0 0 0 0 0 0
0 0 0 0 0 0.23 0.04 - 0.10 0 0 0 0
0 0 0 0 0 0.00 0 0 0.02 0.02 - 0 0.06
Table 5 Results from analysis <strong>of</strong> scenario 1 (after road construction)
Cluster ID c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
Number <strong>of</strong> ponds
in cluster
Number <strong>of</strong> high
quality ponds
(Q> 0.6)
Connectivity to
o<strong>the</strong>r clusters
Estimated cluster
abundance
Mean pond persistence
probability
Connectivity to
c4
Connectivity to
c8
Connectivity to
c11
9 5 2 8 19 13 17 7 6 9 12 5 3
2 0 0 4 2 0 1 7 2 0 3 1 0
0.02 0.10 0.27 0.52 1.69 0.67 1.92 0.23 0.55 0.06 0.09 0.05 0.06
0 0 0 50 2 2 1 24 5 0 49 0 0
0 0 0.03 0.84 0.05 0.24 0.08 0.93 0.26 0 0.78 0 0.15
0 0.08 0 - 0 0.44 0 0 0 0 0 0 0
0 0 0 0 0 0.20 0.01 - 0.02 0 0 0 0
0 0 0 0 0 0 0 0 0.03 0 - 0 0.06
118

Chapter Three
Table 6 Results from analysis <strong>of</strong> mitigation measures.
Scenario 2: Drift fences and underpasses; Scenario 3a: Implementing new ponds in clusters c9
and c11; Scenario 3b: Implementing new ponds as corridor between c9 and c11.
Cluster
ID
Estimated cluster
abundance
Mean pond persistence
probability
Connectivity to c8
Connectivity to c11
S2* S3a S3b S2* S3a S3b S2* S3a S3b S2 S3a S3b
c4 40 48 49 0.82 0.82 0.82 0 0 0 0 0 0
c7 1 3 4 0.08 0.11 0.11
c8
c9
17
(21)
6
(2)
23 23
11 10
0.90
(0.95)
0.38
(0.27)
0.002
(0.004)
0 0 0 0 0
0.90 0.92 - - - 0 0 0
0.44 0.58
0.19
(0.29)
0.02 0.02 0.025 0.03 0.22
c11 40 50 61 0.74 0.80 0.85 0 0 0 - - -
*) In scenario 2 one pond originally belonging to c8 is annexed by c9. Entries in paren<strong>the</strong>ses
are values based on <strong>the</strong> original cluster configurations.
119

Chapter Three
Figure legends
Figure 1:
Location <strong>of</strong> two study areas in Denmark. KaB is an area near Kalundborg on Zealand and
HoB is near Holstebro in Jutland. Only KaB is used in <strong>the</strong> present analysis, but both areas are
used for <strong>the</strong> parameterisation <strong>of</strong> <strong>the</strong> model
Figure 2:
Scenario 0. A) Map <strong>of</strong> <strong>the</strong> landscape before road constructions. Black dots represent potential
breeding ponds. Small dots are ponds with pond quality (Q) ≤ 6; large dots are ponds with Q
≥ 7. Populated ponds are indicated with a star shape.
B) Result <strong>of</strong> cluster analyses showing clusters c1–c13. Ponds linked with black lines belong
to <strong>the</strong> same cluster. Pond size and colour indicate <strong>the</strong> result <strong>of</strong> <strong>the</strong> PopulationDynamics procedure.
Yellow circles represent ponds with an estimated population size ≥ 1. Ponds with larger
yellow circles have a persistence probability > 0.75.
Figure 3:
Scenario 1. A) Map <strong>of</strong> <strong>the</strong> landscape after road constructions (red road). Black dots represent
potential breeding ponds. Small dots are ponds with pond quality (Q) ≤ 6; large dots are ponds
with Q ≥ 7. Populated ponds are indicated with a star shape. Pink ponds are ponds removed in
connection with <strong>the</strong> constructions.
B) Result <strong>of</strong> cluster analyses showing clusters c1–c13. Ponds linked with black lines belong
to <strong>the</strong> same cluster. Pond size and colour indicate <strong>the</strong> result <strong>of</strong> <strong>the</strong> PopulationDynamics procedure.
Yellow circles represent ponds with an estimated population size ≥ 1. Ponds with larger
yellow circles have a persistence probability > 0.75.
Figure 4:
Analyses <strong>of</strong> mitigation measures. Result <strong>of</strong> cluster analyses showing clusters c3–c11. Ponds
linked with black lines belong to <strong>the</strong> same cluster. Pond size and colour indicate <strong>the</strong> result <strong>of</strong>
<strong>the</strong> PopulationDynamics procedure. Yellow circles represent populated ponds. Ponds with
larger yellow circles have a persistence probability > 0.75.
A) Scenario 2 - Location <strong>of</strong> underpasses is shown with red arrows.
B) Scenario 3a – Three new ponds in cluster c9 and five new ponds in c11 are shown with red
dots
C) Scenario 3b – Eight new ponds connecting c9 and c11 are shown with red dots
Figure 5:
Key results from analysis <strong>of</strong> <strong>the</strong> five scenarios. Upper and lower 95% confidence limits are
indicated with black triangles.
120

Chapter Three
Figures
Figure 1
121

Chapter Three
Figure 2
Figure 3
122

Chapter Three
Figure 4
Figure 5
123

Chapter Three
Supplementary material - Appendix 1
Model ODD
Purpose
Road construction and implementation <strong>of</strong> mitigation measures may change landscape features
and <strong>the</strong>reby affect amphibians like <strong>the</strong> Moor frog. The purpose <strong>of</strong> SAIA is to assess how such
changes will influence landscape connectivity and <strong>the</strong> persistence <strong>of</strong> a regional population <strong>of</strong>
Moor frogs. The habitat <strong>of</strong> pond breeding amphibians as <strong>the</strong> Moor frog includes terrestrial as
well as aquatic habitat. Therefore, <strong>the</strong> habitat patch <strong>of</strong> a subpopulation is modelled as a complementary
habitat patch containing not only <strong>the</strong> breeding pond but also all accessible summer
habitat within migration distance from <strong>the</strong> pond (Dunning et al. 1992; Pontoppidan and
Nachman In review; Pope et al. 2000). Immigration, thus, requires two events: 1) <strong>the</strong> successful
dispersal <strong>of</strong> a juvenile frog to summer habitat outside its natal habitat patch and 2) subsequent
successful migration to a breeding pond associated with <strong>the</strong> new summer habitat. In real
life <strong>the</strong>se two events is 2 year apart, but, for simplicity, we only simulate <strong>the</strong> dispersal and
migration events not <strong>the</strong> intervening years.
Entities, state variables, and scales
Breeding ponds are treated as stationary agents. Each pond is characterized by a unique IDnumber,
population size, pond quality, pond perimeter, <strong>the</strong> associated summer habitat and <strong>the</strong>
quality-weighted area <strong>of</strong> <strong>the</strong> summer habitat. Frog agents are characterized by <strong>the</strong> pond in
which <strong>the</strong>y are hatched and <strong>the</strong> breeding pond <strong>the</strong>y immigrate to. The extent <strong>of</strong> <strong>the</strong> model
landscape is 600 x 800 grid cells, and each grid cell is 10 x 10 m. Grid cells are defined by
<strong>the</strong>ir relative attraction to dispersing frogs, habitat survival index and a daily survival probability,
<strong>the</strong> habitat type and <strong>the</strong> cell’s relative value as summer habitat (see Table 1 in main
text). The first part <strong>of</strong> <strong>the</strong> simulation mimics <strong>the</strong> dispersal <strong>of</strong> newly metamorphosed frogs,
starting in mid-summer until hibernation in autumn. The second part considers <strong>the</strong> spring
movement <strong>of</strong> juveniles from <strong>the</strong> summer habitat towards <strong>the</strong>ir future breeding pond and back
to <strong>the</strong>ir summer habitat. Each part runs for 120 time steps, one step representing one day.
124

Chapter Three
Process overview and scheduling
At <strong>the</strong> start <strong>of</strong> a simulation, 250 frog agents are located at each pond agent and <strong>the</strong> frog variable
NatalPond is updated with <strong>the</strong> ID-number <strong>of</strong> <strong>the</strong> pond. In <strong>the</strong> first part <strong>of</strong> <strong>the</strong> simulation
(dispersal) <strong>the</strong> following procedures are executed each time-step: Move (movement <strong>of</strong> frog
agents), Settle (evaluates if a frog agent stops dispersing and assigns frogs to breeding ponds)
and Survival (evaluates if a frog agent survives). At day 120 <strong>the</strong> dispersal stops; frog agents
that have not settled are removed and <strong>the</strong> migration simulation starts. The two procedures
Move and Survival are run every time step and settled frogs start moving again, this time
towards <strong>the</strong>ir breeding pond. When a frog reaches its assigned breeding pond, its direction is
set towards one <strong>of</strong> <strong>the</strong> summer habitat fragments associated with <strong>the</strong> breeding pond. The
simulation stops at day 240 and at each pond <strong>the</strong> model counts <strong>the</strong> number <strong>of</strong> immigrants
from each <strong>of</strong> <strong>the</strong> o<strong>the</strong>r pond agents, computing immigration probabilities between all pairs <strong>of</strong>
ponds. These immigration probabilities <strong>the</strong>n enter <strong>the</strong> population-based PopulationDynamics
(PD) procedure, which is executed. The simulation is repeated 50 times.
Design concepts
Emergence
Immigration rates emerge as a response to <strong>the</strong> landscape configuration.
Adaptation & Objectives
To avoid desiccation and <strong>the</strong>reby increase survival, frog agents are assumed to move in response
to <strong>the</strong> moistness <strong>of</strong> its surroundings. In general, <strong>the</strong> moister a habitat is <strong>the</strong> more attractive
<strong>the</strong> habitat is for <strong>the</strong> frog as indicated by <strong>the</strong> habitat-attraction parameter H a . Dispersing
juvenile Moor frogs have an innate tendency to move away from <strong>the</strong>ir natal pond. Each
frog agent is assigned a random direction to move, but during dispersal <strong>the</strong> frog adjusts its
path to <strong>the</strong> encountered habitat. Adjustments are centred about <strong>the</strong> preferred direction in a
way that prevents backtracking.
Sensing
Frog agents are assumed to be aware <strong>of</strong> <strong>the</strong>ir own state variables. Frog agents are also aware
<strong>of</strong> <strong>the</strong> habitat attraction <strong>of</strong> <strong>the</strong> grid cells as well as <strong>the</strong> identities <strong>of</strong> <strong>the</strong> ponds.
125

Chapter Three
Interaction
There are no interactions between frog agents. Movement decisions <strong>of</strong> <strong>the</strong> frog agents depend
on <strong>the</strong> habitat attraction <strong>of</strong> <strong>the</strong> neighbouring cells. Survival <strong>of</strong> <strong>the</strong> frog agents depends on <strong>the</strong>
daily survival rates associated with <strong>the</strong> traversed habitat. The cell-variables HabitatAttraction
and DailySurvival depend on daily precipitation.
Stochasticity
Which cell to move to is chosen randomly among <strong>the</strong> neighbouring cells with <strong>the</strong> probability
<strong>of</strong> being chosen weighted by <strong>the</strong> habitat attraction <strong>of</strong> <strong>the</strong> neighbouring cells. If frog agents
occupy a cell suitable as summer habitat <strong>the</strong>y will stop dispersing with a certain probability;
<strong>the</strong> probability increases with time. The breeding pond <strong>of</strong> a settled frog is chosen randomly
among accessible breeding ponds weighted by pond-quality. Demographic, but not environmental,
stochasticity is included in <strong>the</strong> PopulationDynamics procedure.
Observation
At <strong>the</strong> end <strong>of</strong> each simulation, <strong>the</strong> natal pond and breeding pond <strong>of</strong> all frog agents are registered
and immigration probabilities (p ij ) between all pair-wise pond agents are calculated. The
PD-procedure is run and <strong>the</strong> estimated population size <strong>of</strong> each pond agent is recorded.
Initialization
A landscape is constructed based on a GIS-raster data set. Each cell contains information
about habitat type, habitat attraction, habitat survival and summer quality. A data set with
information on location, ID-number, pond quality, population size, and pond perimeter <strong>of</strong> <strong>the</strong>
surveyed ponds is used to create pond agents. Once <strong>the</strong> landscape is created, <strong>the</strong> Map-scan
procedure is run to identify all accessible summer habitat associated with each breeding pond
and <strong>the</strong> pond variables A and A’ are updated. Habitat survival is converted to daily survival
probabilities and <strong>the</strong> cell variable D s is updated. A random year is chosen from a climate database
and a data set containing daily precipitation is constructed. 250 frog agents are located
on each pond agent and <strong>the</strong>ir dispersal direction is set randomly. The precipitation threshold α
is set.
Input data
A database containing data on daily precipitation measured in Copenhagen for 21 consecutive
years (1985-2005) is used to reflect natural wea<strong>the</strong>r patterns. At <strong>the</strong> start <strong>of</strong> a simulation, a
126

Chapter Three
random year is chosen from this database and at each time step, information on precipitation
is drawn for <strong>the</strong> simulated day <strong>of</strong> <strong>the</strong> year. Data were supplied by <strong>the</strong> Danish Meteorological
Institute (Cappelen 2009).
Submodels
Map-scan
The cell variable DailySurvival (D s ) is set as <strong>the</strong> probability <strong>of</strong> a frog agent surviving one time
step in <strong>the</strong> cell. This depends on <strong>the</strong> habitat code (H c ) and <strong>the</strong> habitat survival index (H s ) <strong>of</strong>
<strong>the</strong> cell. Cells belonging to <strong>roads</strong>, H c = [2, 3, 4 5] are assigned D s values specific to <strong>the</strong>ir habitat
code (see Appendix 1, Parameterisation). All o<strong>the</strong>r cells are modelled as
1∨ 6 , where σ 0 and σ 1 are species -specific constants.
Local populations <strong>of</strong> pond breeding amphibians inhabit a composite habitat patch. The breeding
pond is located at its core, surrounded by satellites <strong>of</strong> summer habitat fragments separated
by matrix habitat (Pontoppidan and Nachman In review). The Map-scan procedure delimits
<strong>the</strong> extent <strong>of</strong> <strong>the</strong> habitat patch as all accessible cells within a 40-cell (400 m) radius <strong>of</strong> <strong>the</strong>
pond. Accessible cells are defined as cells with habitat attraction (H a ) greater than 1 and daily
survival (D s ) greater than 0.3. This excludes structures such as buildings and large <strong>roads</strong>. Fur<strong>the</strong>rmore,
inaccessible cells function as barriers blocking access to <strong>the</strong> habitat beyond (Eigenbrod
et al. 2008) (Fig. A1). Next, <strong>the</strong> area <strong>of</strong> summer habitat within <strong>the</strong> habitat patch is found.
Summer habitat cells are defined as cells with a summer quality (H q ) higher than 3. A summer
habitat cell can be completely surrounded by o<strong>the</strong>r summer habitat cells (core cells) or have
one or more neighbouring cells which are not summer habitat (edge cells). To account for
edge effects, core cells are given <strong>the</strong> area value (W) <strong>of</strong> 1 while W is 0.5 for edge cells (Watts
and Handley 2010). The effective area <strong>of</strong> <strong>the</strong> summer habitat (A´) within <strong>the</strong> habitat patch is
<strong>the</strong>n computed as:
∑ , where n is <strong>the</strong> number <strong>of</strong> summer habitat cells belonging to <strong>the</strong> habitat
patch and is <strong>the</strong> area value <strong>of</strong> cell i.
Move
Each day frog agents move a randomly chosen distance depending on <strong>the</strong> habitat attraction
(H a ) <strong>of</strong> its current cell. The travelling distance is drawn from a normal distribution with a
mean <strong>of</strong> c and a standard deviation <strong>of</strong> s. Assuming <strong>the</strong> frog to head in <strong>the</strong> direction it was as-
127

Chapter Three
signed when it left <strong>the</strong> natal pond, it moves to one <strong>of</strong> its neighbouring cells located within
±90 0 from <strong>the</strong> preferred direction. Cells with H a = 1 are considered inaccessible. Based on <strong>the</strong>
habitat attraction <strong>of</strong> <strong>the</strong> neighbouring and accessible cells (n), frogs first decide which kind <strong>of</strong>
habitat <strong>the</strong>y want to move to. The probability <strong>of</strong> moving into one <strong>of</strong> <strong>the</strong> cells with habitat attraction
H a is found as
∑
1 , where na is <strong>the</strong> number <strong>of</strong> neighbouring cells
with habitat attraction H a and H ai is <strong>the</strong> habitat attraction <strong>of</strong> cell i. A uniform pseudorandom
number is selected to choose <strong>the</strong> type <strong>of</strong> habitat. If <strong>the</strong>re is more than one neighbouring cell
with <strong>the</strong> chosen habitat attraction, one <strong>of</strong> <strong>the</strong>m is chosen randomly with equal probability. The
frog agent <strong>the</strong>n moves to a random position within <strong>the</strong> cell, without changing its direction.
This routine is repeated until <strong>the</strong> chosen travelling distance for <strong>the</strong> day is traversed. If daily
precipitation exceeds <strong>the</strong> threshold value (α), habitat attraction is inconsequential and <strong>the</strong> frog
moves randomly to one <strong>of</strong> its accessible neighbours.
During <strong>the</strong> second part <strong>of</strong> <strong>the</strong> simulation, as frog agents get within two cells from <strong>the</strong>ir
destination (breeding pond or summer habitat), <strong>the</strong> frogs move directly to it. At <strong>the</strong> breeding
pond, frog agents are randomly assigned a summer habitat cell within <strong>the</strong> habitat patch. When
<strong>the</strong> frogs reach <strong>the</strong>ir summer habitat <strong>the</strong>y stop moving. Frog agents reaching <strong>the</strong> boundary <strong>of</strong>
<strong>the</strong> landscape are removed. If a frog agent does not have an accessible cell within moving
range, its direction is permanently changed ei<strong>the</strong>r 35 degrees to <strong>the</strong> left or to <strong>the</strong> right.
Settle
Dispersing frogs encountering a summer habitat cell have a certain probability <strong>of</strong> settling. The
probability depends on <strong>the</strong> Julian day (t) and is found as:
, where ν 0 and ν 1 are species specific constants
When <strong>the</strong> summer habitat cell in which <strong>the</strong> frog agent has settled is part <strong>of</strong> a habitat patch, <strong>the</strong>
frog is assigned <strong>the</strong> associated breeding pond. If <strong>the</strong> summer habitat cell is shared by several
ponds, <strong>the</strong> probability <strong>of</strong> being assigned a breeding pond i is a function <strong>of</strong> <strong>the</strong> pond quality
(Q) <strong>of</strong> <strong>the</strong> available breeding ponds (n):
until <strong>the</strong> second part <strong>of</strong> <strong>the</strong> simulation.
∑
. Once a frog is settled, it stops moving
128

Chapter Three
Survival
For each frog agent a pseudo-random number is drawn between 0 and 1. If <strong>the</strong> number exceeds
<strong>the</strong> geometric average <strong>of</strong> DailySurvival (D s ) <strong>of</strong> <strong>the</strong> cells traversed during <strong>the</strong> day, <strong>the</strong>
agent dies. When daily precipitation exceeds <strong>the</strong> threshold value (α), D s is temporarily set to
<strong>the</strong> highest value (Table A1), except for cells belonging to <strong>the</strong> road categories, H c = [2, 3, 4
5].
PopulationDynamics (PD)
The PD-procedure estimates frog population size in each pond running through 40 iterations
<strong>of</strong> a life cycle model. The elements <strong>of</strong> <strong>the</strong> life cycle model are 1) Reproduction, 2) Survival
and 3) Immigration. For simplicity we only model <strong>the</strong> female part <strong>of</strong> <strong>the</strong> population. We assume
a sex ratio <strong>of</strong> 0.5 and that females always are mated. Pond populations are grouped by
age 0 through 6 years, and preliminary iterations <strong>of</strong> <strong>the</strong> life cycle produced an estimate <strong>of</strong> <strong>the</strong>
age distribution (see Table 2 in main text). The initial population sizes <strong>of</strong> <strong>the</strong> ponds are <strong>the</strong>
number <strong>of</strong> egg masses found in <strong>the</strong> surveyed ponds (N 0 ). This is expected to equal <strong>the</strong> number
<strong>of</strong> adult females <strong>of</strong> ages 2 - 6. Based on <strong>the</strong> age distribution, <strong>the</strong> initial number <strong>of</strong> frogs <strong>of</strong>
ages 0-6 was estimated and AgeClassList is updated. After each iteration, <strong>the</strong> pond variables
Froglets and AgeClassList are updated with <strong>the</strong> reproductive output and <strong>the</strong> number <strong>of</strong> surviving
individuals in each age class, respectively. The number <strong>of</strong> immigrants is added to age
class 0 in AgeClassList.
Reproduction
The number <strong>of</strong> newly metamorphosed frogs, ready to disperse, is considered to be <strong>the</strong> reproductive
output. This is <strong>the</strong> product <strong>of</strong> egg production, egg and larval survival, as well as <strong>the</strong>
survival <strong>of</strong> <strong>the</strong> frogs <strong>the</strong> first 2 weeks after metamorphosis. The reproductive output is, thus,
modelled as follows. Individuals can reproduce starting at age 3. A mated female produces R
eggs (R = 0, 1, 2 ...) with probability P(R) which is assumed to follow a negative binomial
distribution with mean and clumping parameter k, i.e.
k
k __
(
k R)
k
R
P( R)
__
R k
R k
R k
(R1)
!
varies with age so <strong>the</strong> expected egg production <strong>of</strong> a female <strong>of</strong> age a i is modelled as
129

Chapter Three
(for a ≥3 , o<strong>the</strong>rwise R 0 ) (R2)
where ρ 0 and ρ 1 are parameters expressing <strong>the</strong> effect <strong>of</strong> age on reproduction. R m is <strong>the</strong> reproduction
if ρ 0 = ρ 1 = 0.
The overall probability that an egg develops into a young frog that survives until dispersal
is assumed to be affected by two factors: intraspecific competition and pond quality. Intraspecific
competition is modelled as
ai
F
(R3)
where ψ 0 is a species specific constant and d is egg density in <strong>the</strong> pond. Note that density is
assumed to be proportional with <strong>the</strong> perimeter <strong>of</strong> <strong>the</strong> pond (O) ra<strong>the</strong>r than with <strong>the</strong> area. The
effect <strong>of</strong> pond quality (Q) is modelled as
F
R4
In combination, survival probability until <strong>the</strong> first two weeks after metamorphosis is found as
.
Survival
The conditional probability that a frog survives from age a to age a+1 is assumed to depend
on age, which is modelled with a logistic model as
P
s
0
1a2a
a
1a
2
e
1
e
0 1a
2
2a
S1
where β 0 , β 1 and β 2 are species-specific constants.
Fur<strong>the</strong>rmore, survival is assumed to depend on <strong>the</strong> frog density in <strong>the</strong> summer habitat.
For simplicity, this is modelled as a “culling” process when frog density (D) exceeds <strong>the</strong> carrying
capacity (K j ) <strong>of</strong> summer habitat cell j. K j is determined as WK, where W is <strong>the</strong> cell’s
area value and K is <strong>the</strong> estimated maximum carrying capacity per cell.
Frog density is calculated as ∑
, where h is <strong>the</strong> ponds sharing summer habitat
cell j, and z i is <strong>the</strong> number <strong>of</strong> frogs in age 0 to 6 in pond i divided by <strong>the</strong> number <strong>of</strong> summer
habitat cells belonging to pond i. The number <strong>of</strong> frogs in pond i after “culling” is calculated
as:
130

Chapter Three
∑
, where n is summer habitat cells belonging to pond i, m
j
zi
1
D
j
/ K
j
,
when D j > K j and m j = z i , when D j ≤ K j . Culling is done proportionally on all ages.
Migration
Immigration probabilities between all pairs <strong>of</strong> ponds are obtained from <strong>the</strong> individual based
simulation. The number <strong>of</strong> immigrants (I) arriving at pond i is modelled as:
∑
, where s ij is <strong>the</strong> immigration probability <strong>of</strong> an individual moving from
pond j to pond i and n j is <strong>the</strong> reproductive output <strong>of</strong> pond j given by <strong>the</strong> pond variable Froglets.
Emigration rates are not modelled explicitly.
Parameterisation
All parameter values are listed in table A2.
Habitat attraction (H a )
Terrestrial amphibians are assumed to prefer habitat in which <strong>the</strong> water content is high,
<strong>the</strong>reby minimizing <strong>the</strong> risk <strong>of</strong> desiccation. In an experiment with Nor<strong>the</strong>rn green frogs and
Nor<strong>the</strong>rn leopard frogs in peatlands, Mazerolle and Desrochers (2005) found that 18 out <strong>of</strong> 25
frogs (72%) avoided barren surfaces. Hartung (1991) found that Moor frogs avoided areas
with sparse or low vegetation, and recorded <strong>the</strong> ratio between densities in grass areas and densities
in moor lands, hedges, ditches and forests to be 1:3.5.
In <strong>the</strong> model, <strong>the</strong> probability <strong>of</strong> a frog agent choosing one type <strong>of</strong> cell above ano<strong>the</strong>r
during movement <strong>the</strong>refore depends on <strong>the</strong> attractiveness <strong>of</strong> <strong>the</strong> cell’s habitat type. The habitat
attraction (H a ) <strong>of</strong> <strong>the</strong> different habitat types in <strong>the</strong> GIS maps was approximated by amphibian
specialists (see Table 3 in main text). We tested three different expressions <strong>of</strong> Ha to enter
into <strong>the</strong> Move-procedure: a) H a , b) (H a ) 2 and c) exp(H a ) and compared <strong>the</strong> results with <strong>the</strong>
above-mentioned empirical findings. In addition, we ran a simulation where movement was
independent <strong>of</strong> habitat attraction.
As test landscapes we used GIS data sets from two different road projects in Denmark,
supplied by <strong>the</strong> Danish Road Directorate and Amphi Consult. The first project (KaB) concerns
<strong>the</strong> area described in <strong>the</strong> main text while <strong>the</strong> second project (HoB) is from central Jutland,
ca. 5 km east <strong>of</strong> Holstebro (56° 19.66’ N 8° 44.65’ E N) (Fig. 1). Both areas are charac-
131

Chapter Three
terised as semi-urban and agricultural landscapes, traversed by creeks and wetlands. In <strong>the</strong>
HoB map 36% <strong>of</strong> all cells were classified as attractive habitat (Ha > 3) and <strong>the</strong> KaB map contained
51% attractive habitat cells.
The model was run for 40 time steps without <strong>the</strong> Settle-procedure, and <strong>the</strong> ratio between
frog agents in attractive (H a = 4 or 5) and unattractive (H a = 2 or 3) habitat was computed as
<strong>the</strong> percentage <strong>of</strong> frog agents in attractive habitat. Although <strong>the</strong>re were differences between
<strong>the</strong> maps, we chose <strong>the</strong> expression exp(H a ) as being <strong>the</strong> best to reproduce <strong>the</strong> empirical patterns
(Table A3).
Distance travelled per day
In a radio tracking experiment with Common frogs (Rana temporaria), Tramontano (1997)
found that adult frogs moving through a rye field covered 148 m in one week, corresponding
to ca. 20 m per day. In a study on dispersing juvenile Moor frogs, Hartung (1991) reported
daily travelling distances <strong>of</strong> 12.5 – 18.8 m (mean 15.5) m in attractive habitat (moors) and
39.9 – 40.9 m in unattractive areas (pine forests). The daily travelling distance was thus assumed
to depend on habitat attraction <strong>of</strong> <strong>the</strong> current cell and is modelled as normal distribution
with a mean <strong>of</strong>
and standard deviation s.
Two homogenous landscapes were constructed with a habitat attraction <strong>of</strong> 2 or 4, respectively.
In each landscape frog agents were allowed to move according to <strong>the</strong> Moveprocedure
for 40 time steps. When a simulation ended, <strong>the</strong> straight distances between start and
end point for all frog agents were measured and <strong>the</strong> mean daily travelling distance computed.
The simulations were conducted for varying values <strong>of</strong> c and s, each combination repeated 50
times. A parameter set was sought where <strong>the</strong> daily travelling distance
in attractive habitat takes values between 12 m and 19 m and with a mean around 15 m
in unattractive habitat takes values in <strong>the</strong> range between 20 m and 40 m
The parameter set (c=7, s=0.5) was chosen as <strong>the</strong> one that best fulfilled <strong>the</strong> conditions.
Settle
Few data have been reported on dispersal distances. Hartung (1991) found dispersal distances
<strong>of</strong> newly metamorphosed Moor frogs up to 1200 m, but mean dispersal distance is estimated
by experts to be 200-300 m. As <strong>the</strong> young frogs are assumed to have an innate urge to move
away from <strong>the</strong>ir natal pond, settling probability is expected to be low in <strong>the</strong> beginning. The
132

Chapter Three
dispersal drive is expected to subside with time, with settling probability increasing accordingly,
creating an s-shaped probability function (Fig A2). The realized dispersal distances will
depend on <strong>the</strong> landscape configuration. With <strong>the</strong> chosen parameter set (ν 0 , ν 1 ), <strong>the</strong> mean dispersal
distance <strong>of</strong> frog agents in <strong>the</strong> HoB map is 363 m and <strong>the</strong> maximum dispersal distance is
2068 m. From this, 68% <strong>of</strong> <strong>the</strong> frog agents settle within <strong>the</strong>ir own habitat patch. Less than 2%
<strong>of</strong> <strong>the</strong> frog agents disperse more than 1000 m. In <strong>the</strong> KaB map, <strong>the</strong> mean and maximum dispersal
distances are 291 m and 2151 m, respectively. From this, 83% settle within <strong>the</strong> home
patch and less than 0.5% disperse more than 1000 m (Fig. A3).
Daily survival
The survival probability <strong>of</strong> frogs is assumed to depend on <strong>the</strong> habitat. We were unable to find
any empirical data on daily survival probabilities, but annual survival rates <strong>of</strong> young adult
frogs have been estimated to be between 55% (Fog and Hesselsøe 2009) and 63% (Loman
1984). These rates are not habitat specific but are realised during annual movements in a heterogeneous
landscape.
All land cover categories in GIS maps were ranked according to survivability by amphibian
specialists and assigned a value <strong>of</strong> relative survival index (H s ) (see Table 3 in main
text), which was subsequently converted into daily survival probabilities (D s ). The parameter
set (σ 0 , σ 1 ) gives <strong>the</strong> functional relationship between H s and D s . The parameters were found
by iteration. The model was run with varying combinations <strong>of</strong> parameter values on both test
maps until a set was found for which <strong>the</strong> annual survival rates were between 55% and 63%.
With <strong>the</strong> chosen parameter set, <strong>the</strong> realised annual survival rates were between 56 % and 57
% in both maps. Table A1 shows <strong>the</strong> resulting habitat specific daily survival probabilities.
Road survival
Hels and Buchwald (2001, fig. 5) found <strong>the</strong> probability <strong>of</strong> a Moor frog being killed when
crossing a road ranged from ca. 35% to ca. 90%, depending on traffic intensity. We assumed
traffic intensity to be correlated with road width and let daily survival probability (D s ) depend
on road category as shown in table A4.
PopulationDynamics
Parameterisation <strong>of</strong> reproduction and survival are primarily based on life-table data constructed
by amphibian experts (see Table 2 in main text) as well as experts’ best guesses on
quality-dependent survival (Table A5).
133

Chapter Three
Reproduction and egg survival
The reproduction parameters (R m , ρ 0 , ρ 1 ) are estimated by fitting equation R2 to life-table data
on fecundity (Fig. A4). The estimation <strong>of</strong> clumping factor k is based on data from Lyapkov
(2008) (Table A6).
The quality-dependent survival parameters ψ 1 and ψ 2 are estimated by fitting equation
R4 to data in table A5. These survival rates are expected to be realized only when <strong>the</strong> effect <strong>of</strong>
egg density is negligible. Based on survey data from o<strong>the</strong>r Danish road projects (unpublished),
egg density can be expected to range from 1 to 900 eggs per meter <strong>of</strong> pond perimeter
with a mean density <strong>of</strong> ca. 80 eggs/m. The density-dependent parameter ψ 0 is estimated by
iteration, finding <strong>the</strong> value at which survival probability in high-quality ponds and with an
egg density <strong>of</strong> 1000 eggs/m is ca. 3% (Fig A5).
Frog survival
The survival parameters (β 0 , β 1 , β 2 ) are estimated by fitting equation S1 to life-table data on
survival (Fig. A6). Maximum carrying capacity (K) <strong>of</strong> a summer habitat cell depends on <strong>the</strong>
actual landscape map being analysed and is determined at <strong>the</strong> start <strong>of</strong> <strong>the</strong> PD-procedure as <strong>the</strong>
mean initial frog density <strong>of</strong> summer habitat cells associated with <strong>the</strong> populated ponds.
134

Chapter Three
References
Cappelen J (Ed) (2009) DMI Daily Climate Data Collection 1873-2008, Denmark, The Faroe
Islands and Greenland - including Air Pressure Observations 1874-2008 (WASA Data Sets).
Danish Meteorological Institute, Copenhagen, pp.
Dunning JB, Danielson BJ, Pulliam HR (1992) Ecological processes that affect populations in
complex landscapes. Oikos 65: 169-175. doi:10.2307/3544901
Eigenbrod F, Hecnar SJ, Fahrig L (2008) Accessible habitat: an improved measure <strong>of</strong> <strong>the</strong> effects
<strong>of</strong> habitat loss and <strong>roads</strong> on wildlife populations. Landscape Ecology 23: 159-168.
doi:10.1007/s10980-007-9174-7
Fog K, Hesselsøe M (2009) Udvikling af prototypemodel til brug for forvaltning af
spidssnudet frø i forbindelse med vejanlæg. Amphi Consult, pp.
Hartung H (1991) Untersuchung zur terrestrischen Biologie von Populationen des Moorfrosches
(Rana arvalis NILSSON 1842) unter besonderer Berücksichtigung der Jahresmobilität.
Hamburg: Universität Hamburg.
Hels T, Buchwald E (2001) The effect <strong>of</strong> road kills on amphibian populations. Biological
Conservation 99: 331-340. doi:10.1016/S0006-3207(00)00215-9
Loman J (1984) Density and survival <strong>of</strong> Rana arvalis and Rana temporaria. Alytes 3: 125-
134
Lyapkov SM (2008) A long-term study on <strong>the</strong> population ecology <strong>of</strong> <strong>the</strong> moor frog (Rana
arvalis) in Moscow province, Russia. In: Glandt D, Jehle R (Eds) The Moor Frog Laurenti-
Verlag, Bielefeld, 211-230
Mazerolle MJ, Desrochers A (2005) Landscape resistance to frog movements. Canadian Journal
<strong>of</strong> Zoology-Revue Canadienne De Zoologie 83: 455-464. doi:10.1139/z05-032
Pontoppidan M-B, Nachman G (In review) Effects <strong>of</strong> within-patch heterogeneity on connectivity
in pond-breeding amphibians studied by means <strong>of</strong> an individual-based model. Webecology:
Pope SE, Fahrig L, Merriam NG (2000) Landscape complementation and metapopulation
effects on leopard frog populations. Ecology 81: 2498-2508
Tramontano R (1997) Continuous radio tracking <strong>of</strong> <strong>the</strong> common frog, Rana temporaria. Herpetologia
Bonnensis: 359-365
Watts K, Handley P (2010) Developing a functional connectivity indicator to detect change in
fragmented landscapes. Ecological Indicators 10: 552-557. doi:10.1016/j.ecolind.2009.07.009
135

Chapter Three
Tables
Table A1 Habitat survival index (H s ), <strong>the</strong> corresponding daily survival probability (D s ) and D s
converted into annual survival probability.
H s D s Annual survival probability
1 0.9820 0.01
2 0.9960 0.38
3 0.9984 0.68
4 0.9991 0.81
5 0.9995 0.88
Table A2 List <strong>of</strong> parameters, <strong>the</strong>ir default values and <strong>the</strong> procedure in which <strong>the</strong>y appear
Parameter Value Procedure
ν 0 1.50E-06 Settle
ν 1 0.06 Settle
σ 0 2.2 Map-scan
σ 1 4 Map-scan
τ 0 0.76 Map-scan
τ 1 -5.89 Map-scan
c 7 Move
s 0.5 Move
α 5 mm Move
k 20.5 PD (reproduction)
R m 2.61 PD (reproduction)
ρ 0 0.168 PD (reproduction)
ρ 1 -0.014 PD (reproduction)
ψ 0 0.03 PD (egg survival))
ψ 1 2.20E-05 PD (egg survival)
ψ 2 8.0E-4 PD (egg survival)
β 0 0.1 PD (survival)
β 1 0.28 PD (survival)
β 2 -0.08 PD (survival)
K 0.04 PD (survival)
136

Chapter Three
Table A3 Observed and emerging patterns using three different expressions for entering Ha
into <strong>the</strong> Move procedure as well as random movement independent <strong>of</strong> Ha. Results are shown
for two different maps, Kalundborg (KaB) and Holstebro (HoB)
Pattern
Ratio between
frog densities in
good and bad
habitat (Hartung
1991)
Percentage <strong>of</strong>
individuals
choosing good
habitat (Mazerolle
and Desrochers
2005)
Observed
Random H a H a
2
exp(H a )
KaB HoB KaB HoB KaB HoB KaB HoB
0.29 0.39 0.48 0.46 0.64 0.43 0.53 0.38 0.46
72% 72% 67% 68% 61% 70% 66% 73% 68%
Table A4 Road categories with <strong>the</strong> corresponding habitat code (H c ) and daily survival probability
(D s )
HabitatCode (H c ) Road category D s
2 4-lane motorway 0.1
3 2-lane motorway 0.2
4
5
Road width > 6
m
Road width 3-6
m
0.5
0.8
137

Chapter Three
Table A5 Estimated survival probability from egg until 2 weeks after metamorphosis depending
on pond quality (Q)
Pond quality (Q) Survival probability
0.1 0.00001
0.2 0.00015
0.3 0.00032
0.4 0.00067
0.5 0.0014
0.6 0.003
0.7 0.0064
0.8 0.0136
0.9 0.029
1.0 0.061
Table A6 Age specific mean value <strong>of</strong> fecundity and coefficient <strong>of</strong> variance <strong>of</strong> Rana arvalis
from a study in Moscow, Russia (Lyapkov 2008)
Age
Average number <strong>of</strong>
eggs
3 1057 22,3
4 1193 22,3
5 1267 19,9
6 1332 25,5
Coefficient <strong>of</strong> Variation
(%)
138

Chapter Three
Figures
Figure A1 Illustration <strong>of</strong> how accessible summer habitat is identified.
Blue circle is a pond; dotted circle represents maximum migration distance. Green areas are
accessible summer habitat while shaded areas are inaccessible summer habitat.
A) All summer habitat within migration distance is regarded as accessible
B) Road traversing <strong>the</strong> habitat prevents access to summer habitat on <strong>the</strong> opposite side <strong>of</strong> <strong>the</strong>
road
C) Structures breaking <strong>the</strong> road such as underpasses again permits access to summer habitat
on <strong>the</strong> opposite side <strong>of</strong> <strong>the</strong> road.
A B C
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Chapter Three
Figure A2 Settling probability. If a frog agent encounters a summer habitat cell, <strong>the</strong> probability
<strong>of</strong> settling in <strong>the</strong> cell will depend on day number (Julian day).
1.0
0.8
Settle probability
0.6
0.4
0.2
0.0
170 190 210 230 250 270 290 310
Daynumber
Figure A3 Dispersal distances
The frequency distribution <strong>of</strong> dispersal distances with <strong>the</strong> chosen settling parameters for a)
HoB map b) KaB map. Black line shows accumulated frequencies.
A
B
25
25
20
20
%
15
%
15
10
10
5
5
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Mor
Dispersal distance
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Mor
Dispersal distance (km)
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Chapter Three
Figure A4 Age dependent fecundity
Number <strong>of</strong> produced eggs per female in each age class. Black dots are life table data. Black
line shows <strong>the</strong> modelled function
1300
Number <strong>of</strong> eggs
1200
1100
1000
900
2 3 4 5 6
Age
Figure A5 Egg and larval survival
Survival probabilities as functions <strong>of</strong> pond quality for four different egg densities.
0.06
D1
D100
D500
D1000
Survival probability
0.04
0.02
0.00
0.0 0.2 0.4 0.6 0.8 1.0
Pond quality
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Chapter Three
Figure A6 Adult survival
Age dependent adult survival probability. Black dots are life table data, black line is <strong>the</strong> modelled
function.
0.6
0.5
Survival probability
0.4
0.3
0.2
0 1 2 3 4 5 6
Age class
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SAIA OUTPUT FILES
APPENDIX

144

Appendix
SAIA output files
Text file with descriptive statistics on regional connectivity, abundance and population persistence
probability as well as descriptive statistics on abundance and persistence probability <strong>of</strong>
individual pond populations.
145

Appendix
Text file containing information on clusters and <strong>the</strong>ir pond members as well as connectivity
within and between clusters
146

Appendix
GIS point-data set with information on mean estimated abundance and population persistence
probability <strong>of</strong> <strong>the</strong> ponds. How <strong>the</strong> information is displayed is up to <strong>the</strong> user and <strong>the</strong> facilities
in <strong>the</strong> chosen GIS s<strong>of</strong>tware. Here <strong>the</strong> size <strong>of</strong> <strong>the</strong> dots represents persistence probability and
<strong>the</strong> colour represents estimated population size.
147

Appendix
GIS vector-data set with information about immigration probability between ponds (connectivity
network). Connections are represented as lines, and <strong>the</strong> intensity <strong>of</strong> <strong>the</strong> colour indicates
<strong>the</strong> strength <strong>of</strong> <strong>the</strong> link.
148

Appendix
GIS vector-data set with information about cluster configuration. Black lines connect ponds
belonging to <strong>the</strong> same cluster and cluster-ID is shown beside <strong>the</strong> clusters.
149